{-# 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.Relation.Binary.Lattice 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.Relation.Binary.Bundles
import qualified MAlonzo.Code.Relation.Binary.Structures

-- Relation.Binary.Lattice.Supremum
d_Supremum_12 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Supremum_12 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_Supremum_12 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Relation.Binary.Lattice.Infimum
d_Infimum_30 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Infimum_30 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_Infimum_30 = T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
forall a. a
erased
-- Relation.Binary.Lattice.Exponential
d_Exponential_40 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Exponential_40 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Level_18
d_Exponential_40 = 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
-- Relation.Binary.Lattice.IsJoinSemilattice
d_IsJoinSemilattice_68 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsJoinSemilattice_68 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsJoinSemilattice_68
  = C_IsJoinSemilattice'46'constructor_2281 MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_162
                                            (AgdaAny ->
                                             AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14)
-- Relation.Binary.Lattice.IsJoinSemilattice.isPartialOrder
d_isPartialOrder_88 ::
  T_IsJoinSemilattice_68 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_162
d_isPartialOrder_88 :: T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 T_IsJoinSemilattice_68
v0
  = case T_IsJoinSemilattice_68 -> T_IsJoinSemilattice_68
forall a b. a -> b
coe T_IsJoinSemilattice_68
v0 of
      C_IsJoinSemilattice'46'constructor_2281 T_IsPartialOrder_162
v1 AgdaAny -> AgdaAny -> T_Σ_14
v2 -> T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
v1
      T_IsJoinSemilattice_68
_ -> T_IsPartialOrder_162
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.IsJoinSemilattice.supremum
d_supremum_90 ::
  T_IsJoinSemilattice_68 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_supremum_90 :: T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_90 T_IsJoinSemilattice_68
v0
  = case T_IsJoinSemilattice_68 -> T_IsJoinSemilattice_68
forall a b. a -> b
coe T_IsJoinSemilattice_68
v0 of
      C_IsJoinSemilattice'46'constructor_2281 T_IsPartialOrder_162
v1 AgdaAny -> AgdaAny -> T_Σ_14
v2 -> (AgdaAny -> AgdaAny -> T_Σ_14) -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe AgdaAny -> AgdaAny -> T_Σ_14
v2
      T_IsJoinSemilattice_68
_ -> AgdaAny -> AgdaAny -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.IsJoinSemilattice.x≤x∨y
d_x'8804'x'8744'y_96 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8804'x'8744'y_96 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsJoinSemilattice_68
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8804'x'8744'y_96 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsJoinSemilattice_68
v7 AgdaAny
v8 AgdaAny
v9
  = T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_96 T_IsJoinSemilattice_68
v7 AgdaAny
v8 AgdaAny
v9
du_x'8804'x'8744'y_96 ::
  T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_96 :: T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_96 T_IsJoinSemilattice_68
v0 AgdaAny
v1 AgdaAny
v2
  = (T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28
      ((T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_90 T_IsJoinSemilattice_68
v0 AgdaAny
v1 AgdaAny
v2)
-- Relation.Binary.Lattice.IsJoinSemilattice.y≤x∨y
d_y'8804'x'8744'y_108 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny
d_y'8804'x'8744'y_108 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsJoinSemilattice_68
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_y'8804'x'8744'y_108 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsJoinSemilattice_68
v7 AgdaAny
v8 AgdaAny
v9
  = T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_108 T_IsJoinSemilattice_68
v7 AgdaAny
v8 AgdaAny
v9
du_y'8804'x'8744'y_108 ::
  T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_108 :: T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_108 T_IsJoinSemilattice_68
v0 AgdaAny
v1 AgdaAny
v2
  = (T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28
      ((T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30
         ((T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_90 T_IsJoinSemilattice_68
v0 AgdaAny
v1 AgdaAny
v2))
-- Relation.Binary.Lattice.IsJoinSemilattice.∨-least
d_'8744''45'least_122 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsJoinSemilattice_68 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'least_122 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsJoinSemilattice_68
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'least_122 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsJoinSemilattice_68
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
  = T_IsJoinSemilattice_68
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_122 T_IsJoinSemilattice_68
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
du_'8744''45'least_122 ::
  T_IsJoinSemilattice_68 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_122 :: T_IsJoinSemilattice_68
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_122 T_IsJoinSemilattice_68
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3
  = (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_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30
         ((T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_90 T_IsJoinSemilattice_68
v0 AgdaAny
v1 AgdaAny
v2))
      AgdaAny
v3
-- Relation.Binary.Lattice.IsJoinSemilattice._.antisym
d_antisym_134 ::
  T_IsJoinSemilattice_68 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_134 :: T_IsJoinSemilattice_68
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_134 T_IsJoinSemilattice_68
v0
  = (T_IsPartialOrder_162
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_162
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_172
      ((T_IsJoinSemilattice_68 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 (T_IsJoinSemilattice_68 -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68
v0))
-- Relation.Binary.Lattice.IsJoinSemilattice._.isEquivalence
d_isEquivalence_136 ::
  T_IsJoinSemilattice_68 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_136 :: T_IsJoinSemilattice_68 -> T_IsEquivalence_26
d_isEquivalence_136 T_IsJoinSemilattice_68
v0
  = (T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsJoinSemilattice_68 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 (T_IsJoinSemilattice_68 -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68
v0)))
-- Relation.Binary.Lattice.IsJoinSemilattice._.isPreorder
d_isPreorder_138 ::
  T_IsJoinSemilattice_68 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_138 :: T_IsJoinSemilattice_68 -> T_IsPreorder_70
d_isPreorder_138 T_IsJoinSemilattice_68
v0
  = (T_IsPartialOrder_162 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
      ((T_IsJoinSemilattice_68 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 (T_IsJoinSemilattice_68 -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68
v0))
-- Relation.Binary.Lattice.IsJoinSemilattice._.refl
d_refl_140 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny
d_refl_140 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsJoinSemilattice_68
-> AgdaAny
-> AgdaAny
d_refl_140 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsJoinSemilattice_68
v7 = T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny
du_refl_140 T_IsJoinSemilattice_68
v7
du_refl_140 :: T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny
du_refl_140 :: T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny
du_refl_140 T_IsJoinSemilattice_68
v0
  = let v1 :: T_IsPartialOrder_162
v1 = T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 (T_IsJoinSemilattice_68 -> T_IsJoinSemilattice_68
forall a b. a -> b
coe T_IsJoinSemilattice_68
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsPreorder_70 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_98
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170 (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v1)))
-- Relation.Binary.Lattice.IsJoinSemilattice._.reflexive
d_reflexive_142 ::
  T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_142 :: T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_142 T_IsJoinSemilattice_68
v0
  = (T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsJoinSemilattice_68 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 (T_IsJoinSemilattice_68 -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68
v0)))
-- Relation.Binary.Lattice.IsJoinSemilattice._.trans
d_trans_144 ::
  T_IsJoinSemilattice_68 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_144 :: T_IsJoinSemilattice_68
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_144 T_IsJoinSemilattice_68
v0
  = (T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsJoinSemilattice_68 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 (T_IsJoinSemilattice_68 -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68
v0)))
-- Relation.Binary.Lattice.IsJoinSemilattice._.∼-resp-≈
d_'8764''45'resp'45''8776'_146 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsJoinSemilattice_68 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_146 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsJoinSemilattice_68
-> T_Σ_14
d_'8764''45'resp'45''8776'_146 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsJoinSemilattice_68
v7
  = T_IsJoinSemilattice_68 -> T_Σ_14
du_'8764''45'resp'45''8776'_146 T_IsJoinSemilattice_68
v7
du_'8764''45'resp'45''8776'_146 ::
  T_IsJoinSemilattice_68 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_146 :: T_IsJoinSemilattice_68 -> T_Σ_14
du_'8764''45'resp'45''8776'_146 T_IsJoinSemilattice_68
v0
  = let v1 :: T_IsPartialOrder_162
v1 = T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 (T_IsJoinSemilattice_68 -> T_IsJoinSemilattice_68
forall a b. a -> b
coe T_IsJoinSemilattice_68
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      ((T_IsPreorder_70 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_112
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170 (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v1)))
-- Relation.Binary.Lattice.IsJoinSemilattice._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_148 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsJoinSemilattice_68 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_148 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsJoinSemilattice_68
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_148 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsJoinSemilattice_68
v7
  = T_IsJoinSemilattice_68
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_148 T_IsJoinSemilattice_68
v7
du_'8764''45'resp'691''45''8776'_148 ::
  T_IsJoinSemilattice_68 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_148 :: T_IsJoinSemilattice_68
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_148 T_IsJoinSemilattice_68
v0
  = let v1 :: T_IsPartialOrder_162
v1 = T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 (T_IsJoinSemilattice_68 -> T_IsJoinSemilattice_68
forall a b. a -> b
coe T_IsJoinSemilattice_68
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_106
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170 (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v1)))
-- Relation.Binary.Lattice.IsJoinSemilattice._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_150 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsJoinSemilattice_68 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_150 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsJoinSemilattice_68
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_150 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsJoinSemilattice_68
v7
  = T_IsJoinSemilattice_68
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_150 T_IsJoinSemilattice_68
v7
du_'8764''45'resp'737''45''8776'_150 ::
  T_IsJoinSemilattice_68 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_150 :: T_IsJoinSemilattice_68
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_150 T_IsJoinSemilattice_68
v0
  = let v1 :: T_IsPartialOrder_162
v1 = T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 (T_IsJoinSemilattice_68 -> T_IsJoinSemilattice_68
forall a b. a -> b
coe T_IsJoinSemilattice_68
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_100
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170 (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v1)))
-- Relation.Binary.Lattice.IsJoinSemilattice._.Eq.isPartialEquivalence
d_isPartialEquivalence_154 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsJoinSemilattice_68 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_154 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsJoinSemilattice_68
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_154 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsJoinSemilattice_68
v7
  = T_IsJoinSemilattice_68 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_154 T_IsJoinSemilattice_68
v7
du_isPartialEquivalence_154 ::
  T_IsJoinSemilattice_68 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_154 :: T_IsJoinSemilattice_68 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_154 T_IsJoinSemilattice_68
v0
  = let v1 :: T_IsPartialOrder_162
v1 = T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 (T_IsJoinSemilattice_68 -> T_IsJoinSemilattice_68
forall a b. a -> b
coe T_IsJoinSemilattice_68
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPreorder_70
v2
             = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                 (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
               (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v2))))
-- Relation.Binary.Lattice.IsJoinSemilattice._.Eq.refl
d_refl_156 :: T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny
d_refl_156 :: T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny
d_refl_156 T_IsJoinSemilattice_68
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsJoinSemilattice_68 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 (T_IsJoinSemilattice_68 -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68
v0))))
-- Relation.Binary.Lattice.IsJoinSemilattice._.Eq.reflexive
d_reflexive_158 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsJoinSemilattice_68 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_158 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsJoinSemilattice_68
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_158 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsJoinSemilattice_68
v7
  = T_IsJoinSemilattice_68
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_158 T_IsJoinSemilattice_68
v7
du_reflexive_158 ::
  T_IsJoinSemilattice_68 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_158 :: T_IsJoinSemilattice_68
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_158 T_IsJoinSemilattice_68
v0
  = let v1 :: T_IsPartialOrder_162
v1 = T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 (T_IsJoinSemilattice_68 -> T_IsJoinSemilattice_68
forall a b. a -> b
coe T_IsJoinSemilattice_68
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPreorder_70
v2
             = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                 (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                 (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v2))
              AgdaAny
v3))
-- Relation.Binary.Lattice.IsJoinSemilattice._.Eq.sym
d_sym_160 ::
  T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_160 :: T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_160 T_IsJoinSemilattice_68
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsJoinSemilattice_68 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 (T_IsJoinSemilattice_68 -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68
v0))))
-- Relation.Binary.Lattice.IsJoinSemilattice._.Eq.trans
d_trans_162 ::
  T_IsJoinSemilattice_68 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_162 :: T_IsJoinSemilattice_68
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_162 T_IsJoinSemilattice_68
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsJoinSemilattice_68 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 (T_IsJoinSemilattice_68 -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68
v0))))
-- Relation.Binary.Lattice.JoinSemilattice
d_JoinSemilattice_170 :: p -> p -> p -> T_Level_18
d_JoinSemilattice_170 p
a0 p
a1 p
a2 = ()
data T_JoinSemilattice_170
  = C_JoinSemilattice'46'constructor_7027 (AgdaAny ->
                                           AgdaAny -> AgdaAny)
                                          T_IsJoinSemilattice_68
-- Relation.Binary.Lattice.JoinSemilattice.Carrier
d_Carrier_188 :: T_JoinSemilattice_170 -> ()
d_Carrier_188 :: T_JoinSemilattice_170 -> T_Level_18
d_Carrier_188 = T_JoinSemilattice_170 -> T_Level_18
forall a. a
erased
-- Relation.Binary.Lattice.JoinSemilattice._≈_
d__'8776'__190 :: T_JoinSemilattice_170 -> AgdaAny -> AgdaAny -> ()
d__'8776'__190 :: T_JoinSemilattice_170 -> AgdaAny -> AgdaAny -> T_Level_18
d__'8776'__190 = T_JoinSemilattice_170 -> AgdaAny -> AgdaAny -> T_Level_18
forall a. a
erased
-- Relation.Binary.Lattice.JoinSemilattice._≤_
d__'8804'__192 :: T_JoinSemilattice_170 -> AgdaAny -> AgdaAny -> ()
d__'8804'__192 :: T_JoinSemilattice_170 -> AgdaAny -> AgdaAny -> T_Level_18
d__'8804'__192 = T_JoinSemilattice_170 -> AgdaAny -> AgdaAny -> T_Level_18
forall a. a
erased
-- Relation.Binary.Lattice.JoinSemilattice._∨_
d__'8744'__194 ::
  T_JoinSemilattice_170 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__194 :: T_JoinSemilattice_170 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__194 T_JoinSemilattice_170
v0
  = case T_JoinSemilattice_170 -> T_JoinSemilattice_170
forall a b. a -> b
coe T_JoinSemilattice_170
v0 of
      C_JoinSemilattice'46'constructor_7027 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsJoinSemilattice_68
v5 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_JoinSemilattice_170
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.JoinSemilattice.isJoinSemilattice
d_isJoinSemilattice_196 ::
  T_JoinSemilattice_170 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_196 :: T_JoinSemilattice_170 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_196 T_JoinSemilattice_170
v0
  = case T_JoinSemilattice_170 -> T_JoinSemilattice_170
forall a b. a -> b
coe T_JoinSemilattice_170
v0 of
      C_JoinSemilattice'46'constructor_7027 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsJoinSemilattice_68
v5 -> T_IsJoinSemilattice_68 -> T_IsJoinSemilattice_68
forall a b. a -> b
coe T_IsJoinSemilattice_68
v5
      T_JoinSemilattice_170
_ -> T_IsJoinSemilattice_68
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.JoinSemilattice._.antisym
d_antisym_200 ::
  T_JoinSemilattice_170 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_200 :: T_JoinSemilattice_170
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_200 T_JoinSemilattice_170
v0
  = (T_IsPartialOrder_162
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_162
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_172
      ((T_IsJoinSemilattice_68 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 ((T_JoinSemilattice_170 -> T_IsJoinSemilattice_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_170 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_196 (T_JoinSemilattice_170 -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_170
v0)))
-- Relation.Binary.Lattice.JoinSemilattice._.isEquivalence
d_isEquivalence_202 ::
  T_JoinSemilattice_170 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_202 :: T_JoinSemilattice_170 -> T_IsEquivalence_26
d_isEquivalence_202 T_JoinSemilattice_170
v0
  = (T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsJoinSemilattice_68 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 ((T_JoinSemilattice_170 -> T_IsJoinSemilattice_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_170 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_196 (T_JoinSemilattice_170 -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_170
v0))))
-- Relation.Binary.Lattice.JoinSemilattice._.isPartialOrder
d_isPartialOrder_204 ::
  T_JoinSemilattice_170 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_162
d_isPartialOrder_204 :: T_JoinSemilattice_170 -> T_IsPartialOrder_162
d_isPartialOrder_204 T_JoinSemilattice_170
v0
  = (T_IsJoinSemilattice_68 -> T_IsPartialOrder_162)
-> AgdaAny -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 ((T_JoinSemilattice_170 -> T_IsJoinSemilattice_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_170 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_196 (T_JoinSemilattice_170 -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_170
v0))
-- Relation.Binary.Lattice.JoinSemilattice._.isPreorder
d_isPreorder_206 ::
  T_JoinSemilattice_170 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_206 :: T_JoinSemilattice_170 -> T_IsPreorder_70
d_isPreorder_206 T_JoinSemilattice_170
v0
  = (T_IsPartialOrder_162 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
      ((T_IsJoinSemilattice_68 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 ((T_JoinSemilattice_170 -> T_IsJoinSemilattice_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_170 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_196 (T_JoinSemilattice_170 -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_170
v0)))
-- Relation.Binary.Lattice.JoinSemilattice._.refl
d_refl_208 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_170 -> AgdaAny -> AgdaAny
d_refl_208 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_JoinSemilattice_170
-> AgdaAny
-> AgdaAny
d_refl_208 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_JoinSemilattice_170
v3 = T_JoinSemilattice_170 -> AgdaAny -> AgdaAny
du_refl_208 T_JoinSemilattice_170
v3
du_refl_208 :: T_JoinSemilattice_170 -> AgdaAny -> AgdaAny
du_refl_208 :: T_JoinSemilattice_170 -> AgdaAny -> AgdaAny
du_refl_208 T_JoinSemilattice_170
v0
  = let v1 :: T_IsJoinSemilattice_68
v1 = T_JoinSemilattice_170 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_196 (T_JoinSemilattice_170 -> T_JoinSemilattice_170
forall a b. a -> b
coe T_JoinSemilattice_170
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 (T_IsJoinSemilattice_68 -> T_IsJoinSemilattice_68
forall a b. a -> b
coe T_IsJoinSemilattice_68
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_70 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_98
            ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
               (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v2))))
-- Relation.Binary.Lattice.JoinSemilattice._.reflexive
d_reflexive_210 ::
  T_JoinSemilattice_170 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_210 :: T_JoinSemilattice_170 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_210 T_JoinSemilattice_170
v0
  = (T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsJoinSemilattice_68 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 ((T_JoinSemilattice_170 -> T_IsJoinSemilattice_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_170 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_196 (T_JoinSemilattice_170 -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_170
v0))))
-- Relation.Binary.Lattice.JoinSemilattice._.supremum
d_supremum_212 ::
  T_JoinSemilattice_170 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_supremum_212 :: T_JoinSemilattice_170 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_212 T_JoinSemilattice_170
v0
  = (T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_90 ((T_JoinSemilattice_170 -> T_IsJoinSemilattice_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_170 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_196 (T_JoinSemilattice_170 -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_170
v0))
-- Relation.Binary.Lattice.JoinSemilattice._.trans
d_trans_214 ::
  T_JoinSemilattice_170 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_214 :: T_JoinSemilattice_170
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_214 T_JoinSemilattice_170
v0
  = (T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsJoinSemilattice_68 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 ((T_JoinSemilattice_170 -> T_IsJoinSemilattice_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_170 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_196 (T_JoinSemilattice_170 -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_170
v0))))
-- Relation.Binary.Lattice.JoinSemilattice._.x≤x∨y
d_x'8804'x'8744'y_216 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_170 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8804'x'8744'y_216 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_JoinSemilattice_170
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8804'x'8744'y_216 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_JoinSemilattice_170
v3 = T_JoinSemilattice_170 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_216 T_JoinSemilattice_170
v3
du_x'8804'x'8744'y_216 ::
  T_JoinSemilattice_170 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_216 :: T_JoinSemilattice_170 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_216 T_JoinSemilattice_170
v0
  = (T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_96 ((T_JoinSemilattice_170 -> T_IsJoinSemilattice_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_170 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_196 (T_JoinSemilattice_170 -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_170
v0))
-- Relation.Binary.Lattice.JoinSemilattice._.y≤x∨y
d_y'8804'x'8744'y_218 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_170 -> AgdaAny -> AgdaAny -> AgdaAny
d_y'8804'x'8744'y_218 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_JoinSemilattice_170
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_y'8804'x'8744'y_218 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_JoinSemilattice_170
v3 = T_JoinSemilattice_170 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_218 T_JoinSemilattice_170
v3
du_y'8804'x'8744'y_218 ::
  T_JoinSemilattice_170 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_218 :: T_JoinSemilattice_170 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_218 T_JoinSemilattice_170
v0
  = (T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_108 ((T_JoinSemilattice_170 -> T_IsJoinSemilattice_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_170 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_196 (T_JoinSemilattice_170 -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_170
v0))
-- Relation.Binary.Lattice.JoinSemilattice._.∨-least
d_'8744''45'least_220 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_170 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'least_220 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_JoinSemilattice_170
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'least_220 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_JoinSemilattice_170
v3 = T_JoinSemilattice_170
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_220 T_JoinSemilattice_170
v3
du_'8744''45'least_220 ::
  T_JoinSemilattice_170 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_220 :: T_JoinSemilattice_170
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_220 T_JoinSemilattice_170
v0
  = (T_IsJoinSemilattice_68
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_122 ((T_JoinSemilattice_170 -> T_IsJoinSemilattice_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_170 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_196 (T_JoinSemilattice_170 -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_170
v0))
-- Relation.Binary.Lattice.JoinSemilattice._.∼-resp-≈
d_'8764''45'resp'45''8776'_222 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_170 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_222 :: T_Level_18
-> T_Level_18 -> T_Level_18 -> T_JoinSemilattice_170 -> T_Σ_14
d_'8764''45'resp'45''8776'_222 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_JoinSemilattice_170
v3
  = T_JoinSemilattice_170 -> T_Σ_14
du_'8764''45'resp'45''8776'_222 T_JoinSemilattice_170
v3
du_'8764''45'resp'45''8776'_222 ::
  T_JoinSemilattice_170 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_222 :: T_JoinSemilattice_170 -> T_Σ_14
du_'8764''45'resp'45''8776'_222 T_JoinSemilattice_170
v0
  = let v1 :: T_IsJoinSemilattice_68
v1 = T_JoinSemilattice_170 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_196 (T_JoinSemilattice_170 -> T_JoinSemilattice_170
forall a b. a -> b
coe T_JoinSemilattice_170
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 (T_IsJoinSemilattice_68 -> T_IsJoinSemilattice_68
forall a b. a -> b
coe T_IsJoinSemilattice_68
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_70 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_112
            ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
               (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v2))))
-- Relation.Binary.Lattice.JoinSemilattice._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_224 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_170 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_224 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_JoinSemilattice_170
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_224 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_JoinSemilattice_170
v3
  = T_JoinSemilattice_170
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_224 T_JoinSemilattice_170
v3
du_'8764''45'resp'691''45''8776'_224 ::
  T_JoinSemilattice_170 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_224 :: T_JoinSemilattice_170
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_224 T_JoinSemilattice_170
v0
  = let v1 :: T_IsJoinSemilattice_68
v1 = T_JoinSemilattice_170 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_196 (T_JoinSemilattice_170 -> T_JoinSemilattice_170
forall a b. a -> b
coe T_JoinSemilattice_170
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 (T_IsJoinSemilattice_68 -> T_IsJoinSemilattice_68
forall a b. a -> b
coe T_IsJoinSemilattice_68
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_106
            ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
               (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v2))))
-- Relation.Binary.Lattice.JoinSemilattice._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_226 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_170 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_226 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_JoinSemilattice_170
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_226 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_JoinSemilattice_170
v3
  = T_JoinSemilattice_170
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_226 T_JoinSemilattice_170
v3
du_'8764''45'resp'737''45''8776'_226 ::
  T_JoinSemilattice_170 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_226 :: T_JoinSemilattice_170
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_226 T_JoinSemilattice_170
v0
  = let v1 :: T_IsJoinSemilattice_68
v1 = T_JoinSemilattice_170 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_196 (T_JoinSemilattice_170 -> T_JoinSemilattice_170
forall a b. a -> b
coe T_JoinSemilattice_170
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 (T_IsJoinSemilattice_68 -> T_IsJoinSemilattice_68
forall a b. a -> b
coe T_IsJoinSemilattice_68
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_100
            ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
               (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v2))))
-- Relation.Binary.Lattice.JoinSemilattice._.Eq.isPartialEquivalence
d_isPartialEquivalence_230 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_170 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_230 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_JoinSemilattice_170
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_230 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_JoinSemilattice_170
v3
  = T_JoinSemilattice_170 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_230 T_JoinSemilattice_170
v3
du_isPartialEquivalence_230 ::
  T_JoinSemilattice_170 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_230 :: T_JoinSemilattice_170 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_230 T_JoinSemilattice_170
v0
  = let v1 :: T_IsJoinSemilattice_68
v1 = T_JoinSemilattice_170 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_196 (T_JoinSemilattice_170 -> T_JoinSemilattice_170
forall a b. a -> b
coe T_JoinSemilattice_170
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 (T_IsJoinSemilattice_68 -> T_IsJoinSemilattice_68
forall a b. a -> b
coe T_IsJoinSemilattice_68
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreorder_70
v3
                = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                    (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                  (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v3)))))
-- Relation.Binary.Lattice.JoinSemilattice._.Eq.refl
d_refl_232 :: T_JoinSemilattice_170 -> AgdaAny -> AgdaAny
d_refl_232 :: T_JoinSemilattice_170 -> AgdaAny -> AgdaAny
d_refl_232 T_JoinSemilattice_170
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsJoinSemilattice_68 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 ((T_JoinSemilattice_170 -> T_IsJoinSemilattice_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_170 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_196 (T_JoinSemilattice_170 -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_170
v0)))))
-- Relation.Binary.Lattice.JoinSemilattice._.Eq.reflexive
d_reflexive_234 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_170 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_234 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_JoinSemilattice_170
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_234 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_JoinSemilattice_170
v3 = T_JoinSemilattice_170
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_234 T_JoinSemilattice_170
v3
du_reflexive_234 ::
  T_JoinSemilattice_170 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_234 :: T_JoinSemilattice_170
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_234 T_JoinSemilattice_170
v0
  = let v1 :: T_IsJoinSemilattice_68
v1 = T_JoinSemilattice_170 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_196 (T_JoinSemilattice_170 -> T_JoinSemilattice_170
forall a b. a -> b
coe T_JoinSemilattice_170
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 (T_IsJoinSemilattice_68 -> T_IsJoinSemilattice_68
forall a b. a -> b
coe T_IsJoinSemilattice_68
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreorder_70
v3
                = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                    (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                    (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v3))
                 AgdaAny
v4)))
-- Relation.Binary.Lattice.JoinSemilattice._.Eq.sym
d_sym_236 ::
  T_JoinSemilattice_170 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_236 :: T_JoinSemilattice_170 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_236 T_JoinSemilattice_170
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsJoinSemilattice_68 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 ((T_JoinSemilattice_170 -> T_IsJoinSemilattice_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_170 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_196 (T_JoinSemilattice_170 -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_170
v0)))))
-- Relation.Binary.Lattice.JoinSemilattice._.Eq.trans
d_trans_238 ::
  T_JoinSemilattice_170 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_238 :: T_JoinSemilattice_170
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_238 T_JoinSemilattice_170
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsJoinSemilattice_68 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 ((T_JoinSemilattice_170 -> T_IsJoinSemilattice_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_170 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_196 (T_JoinSemilattice_170 -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_170
v0)))))
-- Relation.Binary.Lattice.JoinSemilattice.poset
d_poset_240 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_170 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Poset_282
d_poset_240 :: T_Level_18
-> T_Level_18 -> T_Level_18 -> T_JoinSemilattice_170 -> T_Poset_282
d_poset_240 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_JoinSemilattice_170
v3 = T_JoinSemilattice_170 -> T_Poset_282
du_poset_240 T_JoinSemilattice_170
v3
du_poset_240 ::
  T_JoinSemilattice_170 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Poset_282
du_poset_240 :: T_JoinSemilattice_170 -> T_Poset_282
du_poset_240 T_JoinSemilattice_170
v0
  = (T_IsPartialOrder_162 -> T_Poset_282)
-> T_IsPartialOrder_162 -> T_Poset_282
forall a b. a -> b
coe
      T_IsPartialOrder_162 -> T_Poset_282
MAlonzo.Code.Relation.Binary.Bundles.C_Poset'46'constructor_5219
      (T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 ((T_JoinSemilattice_170 -> T_IsJoinSemilattice_68)
-> AgdaAny -> T_IsJoinSemilattice_68
forall a b. a -> b
coe T_JoinSemilattice_170 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_196 (T_JoinSemilattice_170 -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_170
v0)))
-- Relation.Binary.Lattice.JoinSemilattice._.preorder
d_preorder_244 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_JoinSemilattice_170 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Preorder_132
d_preorder_244 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_JoinSemilattice_170
-> T_Preorder_132
d_preorder_244 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_JoinSemilattice_170
v3 = T_JoinSemilattice_170 -> T_Preorder_132
du_preorder_244 T_JoinSemilattice_170
v3
du_preorder_244 ::
  T_JoinSemilattice_170 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Preorder_132
du_preorder_244 :: T_JoinSemilattice_170 -> T_Preorder_132
du_preorder_244 T_JoinSemilattice_170
v0
  = (T_Poset_282 -> T_Preorder_132) -> AgdaAny -> T_Preorder_132
forall a b. a -> b
coe
      T_Poset_282 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_326
      ((T_JoinSemilattice_170 -> T_Poset_282) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_170 -> T_Poset_282
du_poset_240 (T_JoinSemilattice_170 -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_170
v0))
-- Relation.Binary.Lattice.IsBoundedJoinSemilattice
d_IsBoundedJoinSemilattice_262 :: p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsBoundedJoinSemilattice_262 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 = ()
data T_IsBoundedJoinSemilattice_262
  = C_IsBoundedJoinSemilattice'46'constructor_9099 T_IsJoinSemilattice_68
                                                   (AgdaAny -> AgdaAny)
-- Relation.Binary.Lattice.IsBoundedJoinSemilattice.isJoinSemilattice
d_isJoinSemilattice_284 ::
  T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284 :: T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284 T_IsBoundedJoinSemilattice_262
v0
  = case T_IsBoundedJoinSemilattice_262 -> T_IsBoundedJoinSemilattice_262
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262
v0 of
      C_IsBoundedJoinSemilattice'46'constructor_9099 T_IsJoinSemilattice_68
v1 AgdaAny -> AgdaAny
v2 -> T_IsJoinSemilattice_68 -> T_IsJoinSemilattice_68
forall a b. a -> b
coe T_IsJoinSemilattice_68
v1
      T_IsBoundedJoinSemilattice_262
_ -> T_IsJoinSemilattice_68
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.IsBoundedJoinSemilattice.minimum
d_minimum_286 ::
  T_IsBoundedJoinSemilattice_262 -> AgdaAny -> AgdaAny
d_minimum_286 :: T_IsBoundedJoinSemilattice_262 -> AgdaAny -> AgdaAny
d_minimum_286 T_IsBoundedJoinSemilattice_262
v0
  = case T_IsBoundedJoinSemilattice_262 -> T_IsBoundedJoinSemilattice_262
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262
v0 of
      C_IsBoundedJoinSemilattice'46'constructor_9099 T_IsJoinSemilattice_68
v1 AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_IsBoundedJoinSemilattice_262
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.IsBoundedJoinSemilattice._.antisym
d_antisym_290 ::
  T_IsBoundedJoinSemilattice_262 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_290 :: T_IsBoundedJoinSemilattice_262
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_290 T_IsBoundedJoinSemilattice_262
v0
  = (T_IsPartialOrder_162
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_162
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_172
      ((T_IsJoinSemilattice_68 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 ((T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284 (T_IsBoundedJoinSemilattice_262 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262
v0)))
-- Relation.Binary.Lattice.IsBoundedJoinSemilattice._.isEquivalence
d_isEquivalence_292 ::
  T_IsBoundedJoinSemilattice_262 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_292 :: T_IsBoundedJoinSemilattice_262 -> T_IsEquivalence_26
d_isEquivalence_292 T_IsBoundedJoinSemilattice_262
v0
  = (T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsJoinSemilattice_68 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 ((T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284 (T_IsBoundedJoinSemilattice_262 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262
v0))))
-- Relation.Binary.Lattice.IsBoundedJoinSemilattice._.isPartialOrder
d_isPartialOrder_294 ::
  T_IsBoundedJoinSemilattice_262 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_162
d_isPartialOrder_294 :: T_IsBoundedJoinSemilattice_262 -> T_IsPartialOrder_162
d_isPartialOrder_294 T_IsBoundedJoinSemilattice_262
v0
  = (T_IsJoinSemilattice_68 -> T_IsPartialOrder_162)
-> AgdaAny -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 ((T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284 (T_IsBoundedJoinSemilattice_262 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262
v0))
-- Relation.Binary.Lattice.IsBoundedJoinSemilattice._.isPreorder
d_isPreorder_296 ::
  T_IsBoundedJoinSemilattice_262 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_296 :: T_IsBoundedJoinSemilattice_262 -> T_IsPreorder_70
d_isPreorder_296 T_IsBoundedJoinSemilattice_262
v0
  = (T_IsPartialOrder_162 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
      ((T_IsJoinSemilattice_68 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 ((T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284 (T_IsBoundedJoinSemilattice_262 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262
v0)))
-- Relation.Binary.Lattice.IsBoundedJoinSemilattice._.refl
d_refl_298 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsBoundedJoinSemilattice_262 -> AgdaAny -> AgdaAny
d_refl_298 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedJoinSemilattice_262
-> AgdaAny
-> AgdaAny
d_refl_298 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedJoinSemilattice_262
v8 = T_IsBoundedJoinSemilattice_262 -> AgdaAny -> AgdaAny
du_refl_298 T_IsBoundedJoinSemilattice_262
v8
du_refl_298 :: T_IsBoundedJoinSemilattice_262 -> AgdaAny -> AgdaAny
du_refl_298 :: T_IsBoundedJoinSemilattice_262 -> AgdaAny -> AgdaAny
du_refl_298 T_IsBoundedJoinSemilattice_262
v0
  = let v1 :: T_IsJoinSemilattice_68
v1 = T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284 (T_IsBoundedJoinSemilattice_262 -> T_IsBoundedJoinSemilattice_262
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 (T_IsJoinSemilattice_68 -> T_IsJoinSemilattice_68
forall a b. a -> b
coe T_IsJoinSemilattice_68
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_70 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_98
            ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
               (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v2))))
-- Relation.Binary.Lattice.IsBoundedJoinSemilattice._.reflexive
d_reflexive_300 ::
  T_IsBoundedJoinSemilattice_262 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_300 :: T_IsBoundedJoinSemilattice_262
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_300 T_IsBoundedJoinSemilattice_262
v0
  = (T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsJoinSemilattice_68 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 ((T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284 (T_IsBoundedJoinSemilattice_262 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262
v0))))
-- Relation.Binary.Lattice.IsBoundedJoinSemilattice._.supremum
d_supremum_302 ::
  T_IsBoundedJoinSemilattice_262 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_supremum_302 :: T_IsBoundedJoinSemilattice_262 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_302 T_IsBoundedJoinSemilattice_262
v0
  = (T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_90 ((T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284 (T_IsBoundedJoinSemilattice_262 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262
v0))
-- Relation.Binary.Lattice.IsBoundedJoinSemilattice._.trans
d_trans_304 ::
  T_IsBoundedJoinSemilattice_262 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_304 :: T_IsBoundedJoinSemilattice_262
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_304 T_IsBoundedJoinSemilattice_262
v0
  = (T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsJoinSemilattice_68 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 ((T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284 (T_IsBoundedJoinSemilattice_262 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262
v0))))
-- Relation.Binary.Lattice.IsBoundedJoinSemilattice._.x≤x∨y
d_x'8804'x'8744'y_306 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsBoundedJoinSemilattice_262 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8804'x'8744'y_306 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedJoinSemilattice_262
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8804'x'8744'y_306 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedJoinSemilattice_262
v8
  = T_IsBoundedJoinSemilattice_262 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_306 T_IsBoundedJoinSemilattice_262
v8
du_x'8804'x'8744'y_306 ::
  T_IsBoundedJoinSemilattice_262 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_306 :: T_IsBoundedJoinSemilattice_262 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_306 T_IsBoundedJoinSemilattice_262
v0
  = (T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_96 ((T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284 (T_IsBoundedJoinSemilattice_262 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262
v0))
-- Relation.Binary.Lattice.IsBoundedJoinSemilattice._.y≤x∨y
d_y'8804'x'8744'y_308 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsBoundedJoinSemilattice_262 -> AgdaAny -> AgdaAny -> AgdaAny
d_y'8804'x'8744'y_308 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedJoinSemilattice_262
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_y'8804'x'8744'y_308 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedJoinSemilattice_262
v8
  = T_IsBoundedJoinSemilattice_262 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_308 T_IsBoundedJoinSemilattice_262
v8
du_y'8804'x'8744'y_308 ::
  T_IsBoundedJoinSemilattice_262 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_308 :: T_IsBoundedJoinSemilattice_262 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_308 T_IsBoundedJoinSemilattice_262
v0
  = (T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_108 ((T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284 (T_IsBoundedJoinSemilattice_262 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262
v0))
-- Relation.Binary.Lattice.IsBoundedJoinSemilattice._.∨-least
d_'8744''45'least_310 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsBoundedJoinSemilattice_262 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'least_310 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedJoinSemilattice_262
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'least_310 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedJoinSemilattice_262
v8
  = T_IsBoundedJoinSemilattice_262
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_310 T_IsBoundedJoinSemilattice_262
v8
du_'8744''45'least_310 ::
  T_IsBoundedJoinSemilattice_262 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_310 :: T_IsBoundedJoinSemilattice_262
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_310 T_IsBoundedJoinSemilattice_262
v0
  = (T_IsJoinSemilattice_68
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_122 ((T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284 (T_IsBoundedJoinSemilattice_262 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262
v0))
-- Relation.Binary.Lattice.IsBoundedJoinSemilattice._.∼-resp-≈
d_'8764''45'resp'45''8776'_312 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsBoundedJoinSemilattice_262 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_312 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedJoinSemilattice_262
-> T_Σ_14
d_'8764''45'resp'45''8776'_312 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedJoinSemilattice_262
v8
  = T_IsBoundedJoinSemilattice_262 -> T_Σ_14
du_'8764''45'resp'45''8776'_312 T_IsBoundedJoinSemilattice_262
v8
du_'8764''45'resp'45''8776'_312 ::
  T_IsBoundedJoinSemilattice_262 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_312 :: T_IsBoundedJoinSemilattice_262 -> T_Σ_14
du_'8764''45'resp'45''8776'_312 T_IsBoundedJoinSemilattice_262
v0
  = let v1 :: T_IsJoinSemilattice_68
v1 = T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284 (T_IsBoundedJoinSemilattice_262 -> T_IsBoundedJoinSemilattice_262
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 (T_IsJoinSemilattice_68 -> T_IsJoinSemilattice_68
forall a b. a -> b
coe T_IsJoinSemilattice_68
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_70 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_112
            ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
               (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v2))))
-- Relation.Binary.Lattice.IsBoundedJoinSemilattice._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_314 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsBoundedJoinSemilattice_262 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_314 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedJoinSemilattice_262
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_314 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7
                                    T_IsBoundedJoinSemilattice_262
v8
  = T_IsBoundedJoinSemilattice_262
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_314 T_IsBoundedJoinSemilattice_262
v8
du_'8764''45'resp'691''45''8776'_314 ::
  T_IsBoundedJoinSemilattice_262 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_314 :: T_IsBoundedJoinSemilattice_262
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_314 T_IsBoundedJoinSemilattice_262
v0
  = let v1 :: T_IsJoinSemilattice_68
v1 = T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284 (T_IsBoundedJoinSemilattice_262 -> T_IsBoundedJoinSemilattice_262
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 (T_IsJoinSemilattice_68 -> T_IsJoinSemilattice_68
forall a b. a -> b
coe T_IsJoinSemilattice_68
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_106
            ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
               (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v2))))
-- Relation.Binary.Lattice.IsBoundedJoinSemilattice._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_316 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsBoundedJoinSemilattice_262 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_316 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedJoinSemilattice_262
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_316 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7
                                    T_IsBoundedJoinSemilattice_262
v8
  = T_IsBoundedJoinSemilattice_262
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_316 T_IsBoundedJoinSemilattice_262
v8
du_'8764''45'resp'737''45''8776'_316 ::
  T_IsBoundedJoinSemilattice_262 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_316 :: T_IsBoundedJoinSemilattice_262
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_316 T_IsBoundedJoinSemilattice_262
v0
  = let v1 :: T_IsJoinSemilattice_68
v1 = T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284 (T_IsBoundedJoinSemilattice_262 -> T_IsBoundedJoinSemilattice_262
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 (T_IsJoinSemilattice_68 -> T_IsJoinSemilattice_68
forall a b. a -> b
coe T_IsJoinSemilattice_68
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_100
            ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
               (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v2))))
-- Relation.Binary.Lattice.IsBoundedJoinSemilattice._.Eq.isPartialEquivalence
d_isPartialEquivalence_320 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsBoundedJoinSemilattice_262 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_320 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedJoinSemilattice_262
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_320 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedJoinSemilattice_262
v8
  = T_IsBoundedJoinSemilattice_262 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_320 T_IsBoundedJoinSemilattice_262
v8
du_isPartialEquivalence_320 ::
  T_IsBoundedJoinSemilattice_262 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_320 :: T_IsBoundedJoinSemilattice_262 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_320 T_IsBoundedJoinSemilattice_262
v0
  = let v1 :: T_IsJoinSemilattice_68
v1 = T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284 (T_IsBoundedJoinSemilattice_262 -> T_IsBoundedJoinSemilattice_262
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 (T_IsJoinSemilattice_68 -> T_IsJoinSemilattice_68
forall a b. a -> b
coe T_IsJoinSemilattice_68
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreorder_70
v3
                = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                    (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                  (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v3)))))
-- Relation.Binary.Lattice.IsBoundedJoinSemilattice._.Eq.refl
d_refl_322 :: T_IsBoundedJoinSemilattice_262 -> AgdaAny -> AgdaAny
d_refl_322 :: T_IsBoundedJoinSemilattice_262 -> AgdaAny -> AgdaAny
d_refl_322 T_IsBoundedJoinSemilattice_262
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsJoinSemilattice_68 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 ((T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284 (T_IsBoundedJoinSemilattice_262 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262
v0)))))
-- Relation.Binary.Lattice.IsBoundedJoinSemilattice._.Eq.reflexive
d_reflexive_324 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsBoundedJoinSemilattice_262 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_324 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedJoinSemilattice_262
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_324 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedJoinSemilattice_262
v8
  = T_IsBoundedJoinSemilattice_262
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_324 T_IsBoundedJoinSemilattice_262
v8
du_reflexive_324 ::
  T_IsBoundedJoinSemilattice_262 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_324 :: T_IsBoundedJoinSemilattice_262
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_324 T_IsBoundedJoinSemilattice_262
v0
  = let v1 :: T_IsJoinSemilattice_68
v1 = T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284 (T_IsBoundedJoinSemilattice_262 -> T_IsBoundedJoinSemilattice_262
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 (T_IsJoinSemilattice_68 -> T_IsJoinSemilattice_68
forall a b. a -> b
coe T_IsJoinSemilattice_68
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreorder_70
v3
                = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                    (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                    (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v3))
                 AgdaAny
v4)))
-- Relation.Binary.Lattice.IsBoundedJoinSemilattice._.Eq.sym
d_sym_326 ::
  T_IsBoundedJoinSemilattice_262 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_326 :: T_IsBoundedJoinSemilattice_262
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_326 T_IsBoundedJoinSemilattice_262
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsJoinSemilattice_68 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 ((T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284 (T_IsBoundedJoinSemilattice_262 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262
v0)))))
-- Relation.Binary.Lattice.IsBoundedJoinSemilattice._.Eq.trans
d_trans_328 ::
  T_IsBoundedJoinSemilattice_262 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_328 :: T_IsBoundedJoinSemilattice_262
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_328 T_IsBoundedJoinSemilattice_262
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsJoinSemilattice_68 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 ((T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284 (T_IsBoundedJoinSemilattice_262 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262
v0)))))
-- Relation.Binary.Lattice.BoundedJoinSemilattice
d_BoundedJoinSemilattice_336 :: p -> p -> p -> T_Level_18
d_BoundedJoinSemilattice_336 p
a0 p
a1 p
a2 = ()
data T_BoundedJoinSemilattice_336
  = C_BoundedJoinSemilattice'46'constructor_11633 (AgdaAny ->
                                                   AgdaAny -> AgdaAny)
                                                  AgdaAny T_IsBoundedJoinSemilattice_262
-- Relation.Binary.Lattice.BoundedJoinSemilattice.Carrier
d_Carrier_356 :: T_BoundedJoinSemilattice_336 -> ()
d_Carrier_356 :: T_BoundedJoinSemilattice_336 -> T_Level_18
d_Carrier_356 = T_BoundedJoinSemilattice_336 -> T_Level_18
forall a. a
erased
-- Relation.Binary.Lattice.BoundedJoinSemilattice._≈_
d__'8776'__358 ::
  T_BoundedJoinSemilattice_336 -> AgdaAny -> AgdaAny -> ()
d__'8776'__358 :: T_BoundedJoinSemilattice_336 -> AgdaAny -> AgdaAny -> T_Level_18
d__'8776'__358 = T_BoundedJoinSemilattice_336 -> AgdaAny -> AgdaAny -> T_Level_18
forall a. a
erased
-- Relation.Binary.Lattice.BoundedJoinSemilattice._≤_
d__'8804'__360 ::
  T_BoundedJoinSemilattice_336 -> AgdaAny -> AgdaAny -> ()
d__'8804'__360 :: T_BoundedJoinSemilattice_336 -> AgdaAny -> AgdaAny -> T_Level_18
d__'8804'__360 = T_BoundedJoinSemilattice_336 -> AgdaAny -> AgdaAny -> T_Level_18
forall a. a
erased
-- Relation.Binary.Lattice.BoundedJoinSemilattice._∨_
d__'8744'__362 ::
  T_BoundedJoinSemilattice_336 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__362 :: T_BoundedJoinSemilattice_336 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__362 T_BoundedJoinSemilattice_336
v0
  = case T_BoundedJoinSemilattice_336 -> T_BoundedJoinSemilattice_336
forall a b. a -> b
coe T_BoundedJoinSemilattice_336
v0 of
      C_BoundedJoinSemilattice'46'constructor_11633 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 T_IsBoundedJoinSemilattice_262
v6 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_BoundedJoinSemilattice_336
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.BoundedJoinSemilattice.⊥
d_'8869'_364 :: T_BoundedJoinSemilattice_336 -> AgdaAny
d_'8869'_364 :: T_BoundedJoinSemilattice_336 -> AgdaAny
d_'8869'_364 T_BoundedJoinSemilattice_336
v0
  = case T_BoundedJoinSemilattice_336 -> T_BoundedJoinSemilattice_336
forall a b. a -> b
coe T_BoundedJoinSemilattice_336
v0 of
      C_BoundedJoinSemilattice'46'constructor_11633 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 T_IsBoundedJoinSemilattice_262
v6 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5
      T_BoundedJoinSemilattice_336
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.BoundedJoinSemilattice.isBoundedJoinSemilattice
d_isBoundedJoinSemilattice_366 ::
  T_BoundedJoinSemilattice_336 -> T_IsBoundedJoinSemilattice_262
d_isBoundedJoinSemilattice_366 :: T_BoundedJoinSemilattice_336 -> T_IsBoundedJoinSemilattice_262
d_isBoundedJoinSemilattice_366 T_BoundedJoinSemilattice_336
v0
  = case T_BoundedJoinSemilattice_336 -> T_BoundedJoinSemilattice_336
forall a b. a -> b
coe T_BoundedJoinSemilattice_336
v0 of
      C_BoundedJoinSemilattice'46'constructor_11633 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 T_IsBoundedJoinSemilattice_262
v6 -> T_IsBoundedJoinSemilattice_262 -> T_IsBoundedJoinSemilattice_262
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262
v6
      T_BoundedJoinSemilattice_336
_ -> T_IsBoundedJoinSemilattice_262
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.BoundedJoinSemilattice._.antisym
d_antisym_370 ::
  T_BoundedJoinSemilattice_336 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_370 :: T_BoundedJoinSemilattice_336
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_370 T_BoundedJoinSemilattice_336
v0
  = (T_IsPartialOrder_162
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_162
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_172
      ((T_IsJoinSemilattice_68 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88
         ((T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284
            ((T_BoundedJoinSemilattice_336 -> T_IsBoundedJoinSemilattice_262)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_336 -> T_IsBoundedJoinSemilattice_262
d_isBoundedJoinSemilattice_366 (T_BoundedJoinSemilattice_336 -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_336
v0))))
-- Relation.Binary.Lattice.BoundedJoinSemilattice._.isEquivalence
d_isEquivalence_372 ::
  T_BoundedJoinSemilattice_336 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_372 :: T_BoundedJoinSemilattice_336 -> T_IsEquivalence_26
d_isEquivalence_372 T_BoundedJoinSemilattice_336
v0
  = (T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsJoinSemilattice_68 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88
            ((T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284
               ((T_BoundedJoinSemilattice_336 -> T_IsBoundedJoinSemilattice_262)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_336 -> T_IsBoundedJoinSemilattice_262
d_isBoundedJoinSemilattice_366 (T_BoundedJoinSemilattice_336 -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_336
v0)))))
-- Relation.Binary.Lattice.BoundedJoinSemilattice._.isJoinSemilattice
d_isJoinSemilattice_374 ::
  T_BoundedJoinSemilattice_336 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_374 :: T_BoundedJoinSemilattice_336 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_374 T_BoundedJoinSemilattice_336
v0
  = (T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68)
-> AgdaAny -> T_IsJoinSemilattice_68
forall a b. a -> b
coe
      T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284
      ((T_BoundedJoinSemilattice_336 -> T_IsBoundedJoinSemilattice_262)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_336 -> T_IsBoundedJoinSemilattice_262
d_isBoundedJoinSemilattice_366 (T_BoundedJoinSemilattice_336 -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_336
v0))
-- Relation.Binary.Lattice.BoundedJoinSemilattice._.isPartialOrder
d_isPartialOrder_376 ::
  T_BoundedJoinSemilattice_336 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_162
d_isPartialOrder_376 :: T_BoundedJoinSemilattice_336 -> T_IsPartialOrder_162
d_isPartialOrder_376 T_BoundedJoinSemilattice_336
v0
  = (T_IsJoinSemilattice_68 -> T_IsPartialOrder_162)
-> AgdaAny -> T_IsPartialOrder_162
forall a b. a -> b
coe
      T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88
      ((T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284
         ((T_BoundedJoinSemilattice_336 -> T_IsBoundedJoinSemilattice_262)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_336 -> T_IsBoundedJoinSemilattice_262
d_isBoundedJoinSemilattice_366 (T_BoundedJoinSemilattice_336 -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_336
v0)))
-- Relation.Binary.Lattice.BoundedJoinSemilattice._.isPreorder
d_isPreorder_378 ::
  T_BoundedJoinSemilattice_336 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_378 :: T_BoundedJoinSemilattice_336 -> T_IsPreorder_70
d_isPreorder_378 T_BoundedJoinSemilattice_336
v0
  = (T_IsPartialOrder_162 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
      ((T_IsJoinSemilattice_68 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88
         ((T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284
            ((T_BoundedJoinSemilattice_336 -> T_IsBoundedJoinSemilattice_262)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_336 -> T_IsBoundedJoinSemilattice_262
d_isBoundedJoinSemilattice_366 (T_BoundedJoinSemilattice_336 -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_336
v0))))
-- Relation.Binary.Lattice.BoundedJoinSemilattice._.minimum
d_minimum_380 :: T_BoundedJoinSemilattice_336 -> AgdaAny -> AgdaAny
d_minimum_380 :: T_BoundedJoinSemilattice_336 -> AgdaAny -> AgdaAny
d_minimum_380 T_BoundedJoinSemilattice_336
v0
  = (T_IsBoundedJoinSemilattice_262 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262 -> AgdaAny -> AgdaAny
d_minimum_286 ((T_BoundedJoinSemilattice_336 -> T_IsBoundedJoinSemilattice_262)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_336 -> T_IsBoundedJoinSemilattice_262
d_isBoundedJoinSemilattice_366 (T_BoundedJoinSemilattice_336 -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_336
v0))
-- Relation.Binary.Lattice.BoundedJoinSemilattice._.refl
d_refl_382 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_336 -> AgdaAny -> AgdaAny
d_refl_382 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedJoinSemilattice_336
-> AgdaAny
-> AgdaAny
d_refl_382 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedJoinSemilattice_336
v3 = T_BoundedJoinSemilattice_336 -> AgdaAny -> AgdaAny
du_refl_382 T_BoundedJoinSemilattice_336
v3
du_refl_382 :: T_BoundedJoinSemilattice_336 -> AgdaAny -> AgdaAny
du_refl_382 :: T_BoundedJoinSemilattice_336 -> AgdaAny -> AgdaAny
du_refl_382 T_BoundedJoinSemilattice_336
v0
  = let v1 :: T_IsBoundedJoinSemilattice_262
v1 = T_BoundedJoinSemilattice_336 -> T_IsBoundedJoinSemilattice_262
d_isBoundedJoinSemilattice_366 (T_BoundedJoinSemilattice_336 -> T_BoundedJoinSemilattice_336
forall a b. a -> b
coe T_BoundedJoinSemilattice_336
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsJoinSemilattice_68
v2 = T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284 (T_IsBoundedJoinSemilattice_262 -> T_IsBoundedJoinSemilattice_262
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3 = T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 (T_IsJoinSemilattice_68 -> T_IsJoinSemilattice_68
forall a b. a -> b
coe T_IsJoinSemilattice_68
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsPreorder_70 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_70 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_98
               ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                  (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v3)))))
-- Relation.Binary.Lattice.BoundedJoinSemilattice._.reflexive
d_reflexive_384 ::
  T_BoundedJoinSemilattice_336 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_384 :: T_BoundedJoinSemilattice_336
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_384 T_BoundedJoinSemilattice_336
v0
  = (T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsJoinSemilattice_68 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88
            ((T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284
               ((T_BoundedJoinSemilattice_336 -> T_IsBoundedJoinSemilattice_262)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_336 -> T_IsBoundedJoinSemilattice_262
d_isBoundedJoinSemilattice_366 (T_BoundedJoinSemilattice_336 -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_336
v0)))))
-- Relation.Binary.Lattice.BoundedJoinSemilattice._.supremum
d_supremum_386 ::
  T_BoundedJoinSemilattice_336 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_supremum_386 :: T_BoundedJoinSemilattice_336 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_386 T_BoundedJoinSemilattice_336
v0
  = (T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_90
      ((T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284
         ((T_BoundedJoinSemilattice_336 -> T_IsBoundedJoinSemilattice_262)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_336 -> T_IsBoundedJoinSemilattice_262
d_isBoundedJoinSemilattice_366 (T_BoundedJoinSemilattice_336 -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_336
v0)))
-- Relation.Binary.Lattice.BoundedJoinSemilattice._.trans
d_trans_388 ::
  T_BoundedJoinSemilattice_336 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_388 :: T_BoundedJoinSemilattice_336
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_388 T_BoundedJoinSemilattice_336
v0
  = (T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsJoinSemilattice_68 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88
            ((T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284
               ((T_BoundedJoinSemilattice_336 -> T_IsBoundedJoinSemilattice_262)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_336 -> T_IsBoundedJoinSemilattice_262
d_isBoundedJoinSemilattice_366 (T_BoundedJoinSemilattice_336 -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_336
v0)))))
-- Relation.Binary.Lattice.BoundedJoinSemilattice._.x≤x∨y
d_x'8804'x'8744'y_390 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_336 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8804'x'8744'y_390 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedJoinSemilattice_336
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8804'x'8744'y_390 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedJoinSemilattice_336
v3 = T_BoundedJoinSemilattice_336 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_390 T_BoundedJoinSemilattice_336
v3
du_x'8804'x'8744'y_390 ::
  T_BoundedJoinSemilattice_336 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_390 :: T_BoundedJoinSemilattice_336 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_390 T_BoundedJoinSemilattice_336
v0
  = let v1 :: T_IsBoundedJoinSemilattice_262
v1 = T_BoundedJoinSemilattice_336 -> T_IsBoundedJoinSemilattice_262
d_isBoundedJoinSemilattice_366 (T_BoundedJoinSemilattice_336 -> T_BoundedJoinSemilattice_336
forall a b. a -> b
coe T_BoundedJoinSemilattice_336
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_96 ((T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284 (T_IsBoundedJoinSemilattice_262 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262
v1)))
-- Relation.Binary.Lattice.BoundedJoinSemilattice._.y≤x∨y
d_y'8804'x'8744'y_392 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_336 -> AgdaAny -> AgdaAny -> AgdaAny
d_y'8804'x'8744'y_392 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedJoinSemilattice_336
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_y'8804'x'8744'y_392 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedJoinSemilattice_336
v3 = T_BoundedJoinSemilattice_336 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_392 T_BoundedJoinSemilattice_336
v3
du_y'8804'x'8744'y_392 ::
  T_BoundedJoinSemilattice_336 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_392 :: T_BoundedJoinSemilattice_336 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_392 T_BoundedJoinSemilattice_336
v0
  = let v1 :: T_IsBoundedJoinSemilattice_262
v1 = T_BoundedJoinSemilattice_336 -> T_IsBoundedJoinSemilattice_262
d_isBoundedJoinSemilattice_366 (T_BoundedJoinSemilattice_336 -> T_BoundedJoinSemilattice_336
forall a b. a -> b
coe T_BoundedJoinSemilattice_336
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_108 ((T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284 (T_IsBoundedJoinSemilattice_262 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262
v1)))
-- Relation.Binary.Lattice.BoundedJoinSemilattice._.∨-least
d_'8744''45'least_394 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_336 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'least_394 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedJoinSemilattice_336
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'least_394 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedJoinSemilattice_336
v3 = T_BoundedJoinSemilattice_336
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_394 T_BoundedJoinSemilattice_336
v3
du_'8744''45'least_394 ::
  T_BoundedJoinSemilattice_336 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_394 :: T_BoundedJoinSemilattice_336
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_394 T_BoundedJoinSemilattice_336
v0
  = let v1 :: T_IsBoundedJoinSemilattice_262
v1 = T_BoundedJoinSemilattice_336 -> T_IsBoundedJoinSemilattice_262
d_isBoundedJoinSemilattice_366 (T_BoundedJoinSemilattice_336 -> T_BoundedJoinSemilattice_336
forall a b. a -> b
coe T_BoundedJoinSemilattice_336
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsJoinSemilattice_68
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_122 ((T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284 (T_IsBoundedJoinSemilattice_262 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262
v1)))
-- Relation.Binary.Lattice.BoundedJoinSemilattice._.∼-resp-≈
d_'8764''45'resp'45''8776'_396 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_336 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_396 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedJoinSemilattice_336
-> T_Σ_14
d_'8764''45'resp'45''8776'_396 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedJoinSemilattice_336
v3
  = T_BoundedJoinSemilattice_336 -> T_Σ_14
du_'8764''45'resp'45''8776'_396 T_BoundedJoinSemilattice_336
v3
du_'8764''45'resp'45''8776'_396 ::
  T_BoundedJoinSemilattice_336 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_396 :: T_BoundedJoinSemilattice_336 -> T_Σ_14
du_'8764''45'resp'45''8776'_396 T_BoundedJoinSemilattice_336
v0
  = let v1 :: T_IsBoundedJoinSemilattice_262
v1 = T_BoundedJoinSemilattice_336 -> T_IsBoundedJoinSemilattice_262
d_isBoundedJoinSemilattice_366 (T_BoundedJoinSemilattice_336 -> T_BoundedJoinSemilattice_336
forall a b. a -> b
coe T_BoundedJoinSemilattice_336
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsJoinSemilattice_68
v2 = T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284 (T_IsBoundedJoinSemilattice_262 -> T_IsBoundedJoinSemilattice_262
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3 = T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 (T_IsJoinSemilattice_68 -> T_IsJoinSemilattice_68
forall a b. a -> b
coe T_IsJoinSemilattice_68
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsPreorder_70 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_70 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_112
               ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                  (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v3)))))
-- Relation.Binary.Lattice.BoundedJoinSemilattice._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_398 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_336 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_398 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedJoinSemilattice_336
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_398 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedJoinSemilattice_336
v3
  = T_BoundedJoinSemilattice_336
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_398 T_BoundedJoinSemilattice_336
v3
du_'8764''45'resp'691''45''8776'_398 ::
  T_BoundedJoinSemilattice_336 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_398 :: T_BoundedJoinSemilattice_336
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_398 T_BoundedJoinSemilattice_336
v0
  = let v1 :: T_IsBoundedJoinSemilattice_262
v1 = T_BoundedJoinSemilattice_336 -> T_IsBoundedJoinSemilattice_262
d_isBoundedJoinSemilattice_366 (T_BoundedJoinSemilattice_336 -> T_BoundedJoinSemilattice_336
forall a b. a -> b
coe T_BoundedJoinSemilattice_336
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsJoinSemilattice_68
v2 = T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284 (T_IsBoundedJoinSemilattice_262 -> T_IsBoundedJoinSemilattice_262
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3 = T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 (T_IsJoinSemilattice_68 -> T_IsJoinSemilattice_68
forall a b. a -> b
coe T_IsJoinSemilattice_68
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_106
               ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                  (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v3)))))
-- Relation.Binary.Lattice.BoundedJoinSemilattice._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_400 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_336 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_400 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedJoinSemilattice_336
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_400 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedJoinSemilattice_336
v3
  = T_BoundedJoinSemilattice_336
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_400 T_BoundedJoinSemilattice_336
v3
du_'8764''45'resp'737''45''8776'_400 ::
  T_BoundedJoinSemilattice_336 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_400 :: T_BoundedJoinSemilattice_336
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_400 T_BoundedJoinSemilattice_336
v0
  = let v1 :: T_IsBoundedJoinSemilattice_262
v1 = T_BoundedJoinSemilattice_336 -> T_IsBoundedJoinSemilattice_262
d_isBoundedJoinSemilattice_366 (T_BoundedJoinSemilattice_336 -> T_BoundedJoinSemilattice_336
forall a b. a -> b
coe T_BoundedJoinSemilattice_336
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsJoinSemilattice_68
v2 = T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284 (T_IsBoundedJoinSemilattice_262 -> T_IsBoundedJoinSemilattice_262
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3 = T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 (T_IsJoinSemilattice_68 -> T_IsJoinSemilattice_68
forall a b. a -> b
coe T_IsJoinSemilattice_68
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_100
               ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                  (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v3)))))
-- Relation.Binary.Lattice.BoundedJoinSemilattice._.Eq.isPartialEquivalence
d_isPartialEquivalence_404 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_336 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_404 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedJoinSemilattice_336
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_404 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedJoinSemilattice_336
v3
  = T_BoundedJoinSemilattice_336 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_404 T_BoundedJoinSemilattice_336
v3
du_isPartialEquivalence_404 ::
  T_BoundedJoinSemilattice_336 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_404 :: T_BoundedJoinSemilattice_336 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_404 T_BoundedJoinSemilattice_336
v0
  = let v1 :: T_IsBoundedJoinSemilattice_262
v1 = T_BoundedJoinSemilattice_336 -> T_IsBoundedJoinSemilattice_262
d_isBoundedJoinSemilattice_366 (T_BoundedJoinSemilattice_336 -> T_BoundedJoinSemilattice_336
forall a b. a -> b
coe T_BoundedJoinSemilattice_336
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsJoinSemilattice_68
v2 = T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284 (T_IsBoundedJoinSemilattice_262 -> T_IsBoundedJoinSemilattice_262
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3 = T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 (T_IsJoinSemilattice_68 -> T_IsJoinSemilattice_68
forall a b. a -> b
coe T_IsJoinSemilattice_68
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreorder_70
v4
                   = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                       (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                     (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v4))))))
-- Relation.Binary.Lattice.BoundedJoinSemilattice._.Eq.refl
d_refl_406 :: T_BoundedJoinSemilattice_336 -> AgdaAny -> AgdaAny
d_refl_406 :: T_BoundedJoinSemilattice_336 -> AgdaAny -> AgdaAny
d_refl_406 T_BoundedJoinSemilattice_336
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsJoinSemilattice_68 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88
               ((T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284
                  ((T_BoundedJoinSemilattice_336 -> T_IsBoundedJoinSemilattice_262)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_336 -> T_IsBoundedJoinSemilattice_262
d_isBoundedJoinSemilattice_366 (T_BoundedJoinSemilattice_336 -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_336
v0))))))
-- Relation.Binary.Lattice.BoundedJoinSemilattice._.Eq.reflexive
d_reflexive_408 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_336 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_408 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedJoinSemilattice_336
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_408 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedJoinSemilattice_336
v3 = T_BoundedJoinSemilattice_336
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_408 T_BoundedJoinSemilattice_336
v3
du_reflexive_408 ::
  T_BoundedJoinSemilattice_336 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_408 :: T_BoundedJoinSemilattice_336
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_408 T_BoundedJoinSemilattice_336
v0
  = let v1 :: T_IsBoundedJoinSemilattice_262
v1 = T_BoundedJoinSemilattice_336 -> T_IsBoundedJoinSemilattice_262
d_isBoundedJoinSemilattice_366 (T_BoundedJoinSemilattice_336 -> T_BoundedJoinSemilattice_336
forall a b. a -> b
coe T_BoundedJoinSemilattice_336
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsJoinSemilattice_68
v2 = T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284 (T_IsBoundedJoinSemilattice_262 -> T_IsBoundedJoinSemilattice_262
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_262
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3 = T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88 (T_IsJoinSemilattice_68 -> T_IsJoinSemilattice_68
forall a b. a -> b
coe T_IsJoinSemilattice_68
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreorder_70
v4
                   = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                       (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                       (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v4))
                    AgdaAny
v5))))
-- Relation.Binary.Lattice.BoundedJoinSemilattice._.Eq.sym
d_sym_410 ::
  T_BoundedJoinSemilattice_336 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_410 :: T_BoundedJoinSemilattice_336
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_410 T_BoundedJoinSemilattice_336
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsJoinSemilattice_68 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88
               ((T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284
                  ((T_BoundedJoinSemilattice_336 -> T_IsBoundedJoinSemilattice_262)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_336 -> T_IsBoundedJoinSemilattice_262
d_isBoundedJoinSemilattice_366 (T_BoundedJoinSemilattice_336 -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_336
v0))))))
-- Relation.Binary.Lattice.BoundedJoinSemilattice._.Eq.trans
d_trans_412 ::
  T_BoundedJoinSemilattice_336 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_412 :: T_BoundedJoinSemilattice_336
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_412 T_BoundedJoinSemilattice_336
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsJoinSemilattice_68 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsJoinSemilattice_68 -> T_IsPartialOrder_162
d_isPartialOrder_88
               ((T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284
                  ((T_BoundedJoinSemilattice_336 -> T_IsBoundedJoinSemilattice_262)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_336 -> T_IsBoundedJoinSemilattice_262
d_isBoundedJoinSemilattice_366 (T_BoundedJoinSemilattice_336 -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_336
v0))))))
-- Relation.Binary.Lattice.BoundedJoinSemilattice.joinSemilattice
d_joinSemilattice_414 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_336 -> T_JoinSemilattice_170
d_joinSemilattice_414 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedJoinSemilattice_336
-> T_JoinSemilattice_170
d_joinSemilattice_414 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedJoinSemilattice_336
v3 = T_BoundedJoinSemilattice_336 -> T_JoinSemilattice_170
du_joinSemilattice_414 T_BoundedJoinSemilattice_336
v3
du_joinSemilattice_414 ::
  T_BoundedJoinSemilattice_336 -> T_JoinSemilattice_170
du_joinSemilattice_414 :: T_BoundedJoinSemilattice_336 -> T_JoinSemilattice_170
du_joinSemilattice_414 T_BoundedJoinSemilattice_336
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsJoinSemilattice_68 -> T_JoinSemilattice_170)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsJoinSemilattice_68
-> T_JoinSemilattice_170
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsJoinSemilattice_68 -> T_JoinSemilattice_170
C_JoinSemilattice'46'constructor_7027 (T_BoundedJoinSemilattice_336 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__362 (T_BoundedJoinSemilattice_336 -> T_BoundedJoinSemilattice_336
forall a b. a -> b
coe T_BoundedJoinSemilattice_336
v0))
      (T_IsBoundedJoinSemilattice_262 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_284
         ((T_BoundedJoinSemilattice_336 -> T_IsBoundedJoinSemilattice_262)
-> AgdaAny -> T_IsBoundedJoinSemilattice_262
forall a b. a -> b
coe T_BoundedJoinSemilattice_336 -> T_IsBoundedJoinSemilattice_262
d_isBoundedJoinSemilattice_366 (T_BoundedJoinSemilattice_336 -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_336
v0)))
-- Relation.Binary.Lattice.BoundedJoinSemilattice.joinSemiLattice
d_joinSemiLattice_416 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_336 -> T_JoinSemilattice_170
d_joinSemiLattice_416 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedJoinSemilattice_336
-> T_JoinSemilattice_170
d_joinSemiLattice_416 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedJoinSemilattice_336
v3 = T_BoundedJoinSemilattice_336 -> T_JoinSemilattice_170
du_joinSemiLattice_416 T_BoundedJoinSemilattice_336
v3
du_joinSemiLattice_416 ::
  T_BoundedJoinSemilattice_336 -> T_JoinSemilattice_170
du_joinSemiLattice_416 :: T_BoundedJoinSemilattice_336 -> T_JoinSemilattice_170
du_joinSemiLattice_416 T_BoundedJoinSemilattice_336
v0 = (T_BoundedJoinSemilattice_336 -> T_JoinSemilattice_170)
-> AgdaAny -> T_JoinSemilattice_170
forall a b. a -> b
coe T_BoundedJoinSemilattice_336 -> T_JoinSemilattice_170
du_joinSemilattice_414 (T_BoundedJoinSemilattice_336 -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_336
v0)
-- Relation.Binary.Lattice.BoundedJoinSemilattice._.poset
d_poset_420 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_336 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Poset_282
d_poset_420 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedJoinSemilattice_336
-> T_Poset_282
d_poset_420 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedJoinSemilattice_336
v3 = T_BoundedJoinSemilattice_336 -> T_Poset_282
du_poset_420 T_BoundedJoinSemilattice_336
v3
du_poset_420 ::
  T_BoundedJoinSemilattice_336 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Poset_282
du_poset_420 :: T_BoundedJoinSemilattice_336 -> T_Poset_282
du_poset_420 T_BoundedJoinSemilattice_336
v0
  = (T_JoinSemilattice_170 -> T_Poset_282) -> AgdaAny -> T_Poset_282
forall a b. a -> b
coe T_JoinSemilattice_170 -> T_Poset_282
du_poset_240 ((T_BoundedJoinSemilattice_336 -> T_JoinSemilattice_170)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_336 -> T_JoinSemilattice_170
du_joinSemilattice_414 (T_BoundedJoinSemilattice_336 -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_336
v0))
-- Relation.Binary.Lattice.BoundedJoinSemilattice._.preorder
d_preorder_422 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedJoinSemilattice_336 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Preorder_132
d_preorder_422 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedJoinSemilattice_336
-> T_Preorder_132
d_preorder_422 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedJoinSemilattice_336
v3 = T_BoundedJoinSemilattice_336 -> T_Preorder_132
du_preorder_422 T_BoundedJoinSemilattice_336
v3
du_preorder_422 ::
  T_BoundedJoinSemilattice_336 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Preorder_132
du_preorder_422 :: T_BoundedJoinSemilattice_336 -> T_Preorder_132
du_preorder_422 T_BoundedJoinSemilattice_336
v0
  = let v1 :: t
v1 = (T_BoundedJoinSemilattice_336 -> T_JoinSemilattice_170)
-> AgdaAny -> t
forall a b. a -> b
coe T_BoundedJoinSemilattice_336 -> T_JoinSemilattice_170
du_joinSemilattice_414 (T_BoundedJoinSemilattice_336 -> AgdaAny
forall a b. a -> b
coe T_BoundedJoinSemilattice_336
v0) in
    AgdaAny -> T_Preorder_132
forall a b. a -> b
coe
      ((T_Poset_282 -> T_Preorder_132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Poset_282 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_326
         ((T_JoinSemilattice_170 -> T_Poset_282) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_170 -> T_Poset_282
du_poset_240 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Relation.Binary.Lattice.IsMeetSemilattice
d_IsMeetSemilattice_438 :: p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsMeetSemilattice_438 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsMeetSemilattice_438
  = C_IsMeetSemilattice'46'constructor_13939 MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_162
                                             (AgdaAny ->
                                              AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14)
-- Relation.Binary.Lattice.IsMeetSemilattice.isPartialOrder
d_isPartialOrder_458 ::
  T_IsMeetSemilattice_438 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_162
d_isPartialOrder_458 :: T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 T_IsMeetSemilattice_438
v0
  = case T_IsMeetSemilattice_438 -> T_IsMeetSemilattice_438
forall a b. a -> b
coe T_IsMeetSemilattice_438
v0 of
      C_IsMeetSemilattice'46'constructor_13939 T_IsPartialOrder_162
v1 AgdaAny -> AgdaAny -> T_Σ_14
v2 -> T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
v1
      T_IsMeetSemilattice_438
_ -> T_IsPartialOrder_162
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.IsMeetSemilattice.infimum
d_infimum_460 ::
  T_IsMeetSemilattice_438 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_infimum_460 :: T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_460 T_IsMeetSemilattice_438
v0
  = case T_IsMeetSemilattice_438 -> T_IsMeetSemilattice_438
forall a b. a -> b
coe T_IsMeetSemilattice_438
v0 of
      C_IsMeetSemilattice'46'constructor_13939 T_IsPartialOrder_162
v1 AgdaAny -> AgdaAny -> T_Σ_14
v2 -> (AgdaAny -> AgdaAny -> T_Σ_14) -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe AgdaAny -> AgdaAny -> T_Σ_14
v2
      T_IsMeetSemilattice_438
_ -> AgdaAny -> AgdaAny -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.IsMeetSemilattice.x∧y≤x
d_x'8743'y'8804'x_466 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'x_466 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMeetSemilattice_438
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'x_466 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsMeetSemilattice_438
v7 AgdaAny
v8 AgdaAny
v9
  = T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_466 T_IsMeetSemilattice_438
v7 AgdaAny
v8 AgdaAny
v9
du_x'8743'y'8804'x_466 ::
  T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_466 :: T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_466 T_IsMeetSemilattice_438
v0 AgdaAny
v1 AgdaAny
v2
  = (T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28
      ((T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_460 T_IsMeetSemilattice_438
v0 AgdaAny
v1 AgdaAny
v2)
-- Relation.Binary.Lattice.IsMeetSemilattice.x∧y≤y
d_x'8743'y'8804'y_478 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'y_478 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMeetSemilattice_438
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'y_478 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsMeetSemilattice_438
v7 AgdaAny
v8 AgdaAny
v9
  = T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_478 T_IsMeetSemilattice_438
v7 AgdaAny
v8 AgdaAny
v9
du_x'8743'y'8804'y_478 ::
  T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_478 :: T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_478 T_IsMeetSemilattice_438
v0 AgdaAny
v1 AgdaAny
v2
  = (T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_fst_28
      ((T_Σ_14 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30
         ((T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_460 T_IsMeetSemilattice_438
v0 AgdaAny
v1 AgdaAny
v2))
-- Relation.Binary.Lattice.IsMeetSemilattice.∧-greatest
d_'8743''45'greatest_492 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMeetSemilattice_438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'greatest_492 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMeetSemilattice_438
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'greatest_492 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsMeetSemilattice_438
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
  = T_IsMeetSemilattice_438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_492 T_IsMeetSemilattice_438
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
du_'8743''45'greatest_492 ::
  T_IsMeetSemilattice_438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_492 :: T_IsMeetSemilattice_438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_492 T_IsMeetSemilattice_438
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3
  = (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_Σ_14 -> AgdaAny
MAlonzo.Code.Agda.Builtin.Sigma.d_snd_30
         ((T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_460 T_IsMeetSemilattice_438
v0 AgdaAny
v2 AgdaAny
v3))
      AgdaAny
v1
-- Relation.Binary.Lattice.IsMeetSemilattice._.antisym
d_antisym_504 ::
  T_IsMeetSemilattice_438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_504 :: T_IsMeetSemilattice_438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_504 T_IsMeetSemilattice_438
v0
  = (T_IsPartialOrder_162
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_162
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_172
      ((T_IsMeetSemilattice_438 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 (T_IsMeetSemilattice_438 -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_438
v0))
-- Relation.Binary.Lattice.IsMeetSemilattice._.isEquivalence
d_isEquivalence_506 ::
  T_IsMeetSemilattice_438 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_506 :: T_IsMeetSemilattice_438 -> T_IsEquivalence_26
d_isEquivalence_506 T_IsMeetSemilattice_438
v0
  = (T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsMeetSemilattice_438 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 (T_IsMeetSemilattice_438 -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_438
v0)))
-- Relation.Binary.Lattice.IsMeetSemilattice._.isPreorder
d_isPreorder_508 ::
  T_IsMeetSemilattice_438 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_508 :: T_IsMeetSemilattice_438 -> T_IsPreorder_70
d_isPreorder_508 T_IsMeetSemilattice_438
v0
  = (T_IsPartialOrder_162 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
      ((T_IsMeetSemilattice_438 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 (T_IsMeetSemilattice_438 -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_438
v0))
-- Relation.Binary.Lattice.IsMeetSemilattice._.refl
d_refl_510 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny
d_refl_510 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMeetSemilattice_438
-> AgdaAny
-> AgdaAny
d_refl_510 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsMeetSemilattice_438
v7 = T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny
du_refl_510 T_IsMeetSemilattice_438
v7
du_refl_510 :: T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny
du_refl_510 :: T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny
du_refl_510 T_IsMeetSemilattice_438
v0
  = let v1 :: T_IsPartialOrder_162
v1 = T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 (T_IsMeetSemilattice_438 -> T_IsMeetSemilattice_438
forall a b. a -> b
coe T_IsMeetSemilattice_438
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsPreorder_70 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_98
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170 (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v1)))
-- Relation.Binary.Lattice.IsMeetSemilattice._.reflexive
d_reflexive_512 ::
  T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_512 :: T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_512 T_IsMeetSemilattice_438
v0
  = (T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsMeetSemilattice_438 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 (T_IsMeetSemilattice_438 -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_438
v0)))
-- Relation.Binary.Lattice.IsMeetSemilattice._.trans
d_trans_514 ::
  T_IsMeetSemilattice_438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_514 :: T_IsMeetSemilattice_438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_514 T_IsMeetSemilattice_438
v0
  = (T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsMeetSemilattice_438 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 (T_IsMeetSemilattice_438 -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_438
v0)))
-- Relation.Binary.Lattice.IsMeetSemilattice._.∼-resp-≈
d_'8764''45'resp'45''8776'_516 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMeetSemilattice_438 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_516 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMeetSemilattice_438
-> T_Σ_14
d_'8764''45'resp'45''8776'_516 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsMeetSemilattice_438
v7
  = T_IsMeetSemilattice_438 -> T_Σ_14
du_'8764''45'resp'45''8776'_516 T_IsMeetSemilattice_438
v7
du_'8764''45'resp'45''8776'_516 ::
  T_IsMeetSemilattice_438 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_516 :: T_IsMeetSemilattice_438 -> T_Σ_14
du_'8764''45'resp'45''8776'_516 T_IsMeetSemilattice_438
v0
  = let v1 :: T_IsPartialOrder_162
v1 = T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 (T_IsMeetSemilattice_438 -> T_IsMeetSemilattice_438
forall a b. a -> b
coe T_IsMeetSemilattice_438
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      ((T_IsPreorder_70 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_112
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170 (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v1)))
-- Relation.Binary.Lattice.IsMeetSemilattice._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_518 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMeetSemilattice_438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_518 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMeetSemilattice_438
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_518 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsMeetSemilattice_438
v7
  = T_IsMeetSemilattice_438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_518 T_IsMeetSemilattice_438
v7
du_'8764''45'resp'691''45''8776'_518 ::
  T_IsMeetSemilattice_438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_518 :: T_IsMeetSemilattice_438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_518 T_IsMeetSemilattice_438
v0
  = let v1 :: T_IsPartialOrder_162
v1 = T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 (T_IsMeetSemilattice_438 -> T_IsMeetSemilattice_438
forall a b. a -> b
coe T_IsMeetSemilattice_438
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_106
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170 (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v1)))
-- Relation.Binary.Lattice.IsMeetSemilattice._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_520 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMeetSemilattice_438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_520 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMeetSemilattice_438
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_520 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsMeetSemilattice_438
v7
  = T_IsMeetSemilattice_438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_520 T_IsMeetSemilattice_438
v7
du_'8764''45'resp'737''45''8776'_520 ::
  T_IsMeetSemilattice_438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_520 :: T_IsMeetSemilattice_438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_520 T_IsMeetSemilattice_438
v0
  = let v1 :: T_IsPartialOrder_162
v1 = T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 (T_IsMeetSemilattice_438 -> T_IsMeetSemilattice_438
forall a b. a -> b
coe T_IsMeetSemilattice_438
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_100
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170 (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v1)))
-- Relation.Binary.Lattice.IsMeetSemilattice._.Eq.isPartialEquivalence
d_isPartialEquivalence_524 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMeetSemilattice_438 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_524 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMeetSemilattice_438
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_524 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsMeetSemilattice_438
v7
  = T_IsMeetSemilattice_438 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_524 T_IsMeetSemilattice_438
v7
du_isPartialEquivalence_524 ::
  T_IsMeetSemilattice_438 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_524 :: T_IsMeetSemilattice_438 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_524 T_IsMeetSemilattice_438
v0
  = let v1 :: T_IsPartialOrder_162
v1 = T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 (T_IsMeetSemilattice_438 -> T_IsMeetSemilattice_438
forall a b. a -> b
coe T_IsMeetSemilattice_438
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPreorder_70
v2
             = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                 (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
               (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v2))))
-- Relation.Binary.Lattice.IsMeetSemilattice._.Eq.refl
d_refl_526 :: T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny
d_refl_526 :: T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny
d_refl_526 T_IsMeetSemilattice_438
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsMeetSemilattice_438 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 (T_IsMeetSemilattice_438 -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_438
v0))))
-- Relation.Binary.Lattice.IsMeetSemilattice._.Eq.reflexive
d_reflexive_528 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsMeetSemilattice_438 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_528 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMeetSemilattice_438
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_528 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsMeetSemilattice_438
v7
  = T_IsMeetSemilattice_438
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_528 T_IsMeetSemilattice_438
v7
du_reflexive_528 ::
  T_IsMeetSemilattice_438 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_528 :: T_IsMeetSemilattice_438
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_528 T_IsMeetSemilattice_438
v0
  = let v1 :: T_IsPartialOrder_162
v1 = T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 (T_IsMeetSemilattice_438 -> T_IsMeetSemilattice_438
forall a b. a -> b
coe T_IsMeetSemilattice_438
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPreorder_70
v2
             = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                 (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                 (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v2))
              AgdaAny
v3))
-- Relation.Binary.Lattice.IsMeetSemilattice._.Eq.sym
d_sym_530 ::
  T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_530 :: T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_530 T_IsMeetSemilattice_438
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsMeetSemilattice_438 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 (T_IsMeetSemilattice_438 -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_438
v0))))
-- Relation.Binary.Lattice.IsMeetSemilattice._.Eq.trans
d_trans_532 ::
  T_IsMeetSemilattice_438 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_532 :: T_IsMeetSemilattice_438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_532 T_IsMeetSemilattice_438
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsMeetSemilattice_438 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 (T_IsMeetSemilattice_438 -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_438
v0))))
-- Relation.Binary.Lattice.MeetSemilattice
d_MeetSemilattice_540 :: p -> p -> p -> T_Level_18
d_MeetSemilattice_540 p
a0 p
a1 p
a2 = ()
data T_MeetSemilattice_540
  = C_MeetSemilattice'46'constructor_18685 (AgdaAny ->
                                            AgdaAny -> AgdaAny)
                                           T_IsMeetSemilattice_438
-- Relation.Binary.Lattice.MeetSemilattice.Carrier
d_Carrier_558 :: T_MeetSemilattice_540 -> ()
d_Carrier_558 :: T_MeetSemilattice_540 -> T_Level_18
d_Carrier_558 = T_MeetSemilattice_540 -> T_Level_18
forall a. a
erased
-- Relation.Binary.Lattice.MeetSemilattice._≈_
d__'8776'__560 :: T_MeetSemilattice_540 -> AgdaAny -> AgdaAny -> ()
d__'8776'__560 :: T_MeetSemilattice_540 -> AgdaAny -> AgdaAny -> T_Level_18
d__'8776'__560 = T_MeetSemilattice_540 -> AgdaAny -> AgdaAny -> T_Level_18
forall a. a
erased
-- Relation.Binary.Lattice.MeetSemilattice._≤_
d__'8804'__562 :: T_MeetSemilattice_540 -> AgdaAny -> AgdaAny -> ()
d__'8804'__562 :: T_MeetSemilattice_540 -> AgdaAny -> AgdaAny -> T_Level_18
d__'8804'__562 = T_MeetSemilattice_540 -> AgdaAny -> AgdaAny -> T_Level_18
forall a. a
erased
-- Relation.Binary.Lattice.MeetSemilattice._∧_
d__'8743'__564 ::
  T_MeetSemilattice_540 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__564 :: T_MeetSemilattice_540 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__564 T_MeetSemilattice_540
v0
  = case T_MeetSemilattice_540 -> T_MeetSemilattice_540
forall a b. a -> b
coe T_MeetSemilattice_540
v0 of
      C_MeetSemilattice'46'constructor_18685 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMeetSemilattice_438
v5 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_MeetSemilattice_540
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.MeetSemilattice.isMeetSemilattice
d_isMeetSemilattice_566 ::
  T_MeetSemilattice_540 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_566 :: T_MeetSemilattice_540 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_566 T_MeetSemilattice_540
v0
  = case T_MeetSemilattice_540 -> T_MeetSemilattice_540
forall a b. a -> b
coe T_MeetSemilattice_540
v0 of
      C_MeetSemilattice'46'constructor_18685 AgdaAny -> AgdaAny -> AgdaAny
v4 T_IsMeetSemilattice_438
v5 -> T_IsMeetSemilattice_438 -> T_IsMeetSemilattice_438
forall a b. a -> b
coe T_IsMeetSemilattice_438
v5
      T_MeetSemilattice_540
_ -> T_IsMeetSemilattice_438
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.MeetSemilattice._.antisym
d_antisym_570 ::
  T_MeetSemilattice_540 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_570 :: T_MeetSemilattice_540
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_570 T_MeetSemilattice_540
v0
  = (T_IsPartialOrder_162
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_162
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_172
      ((T_IsMeetSemilattice_438 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 ((T_MeetSemilattice_540 -> T_IsMeetSemilattice_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_540 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_566 (T_MeetSemilattice_540 -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_540
v0)))
-- Relation.Binary.Lattice.MeetSemilattice._.infimum
d_infimum_572 ::
  T_MeetSemilattice_540 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_infimum_572 :: T_MeetSemilattice_540 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_572 T_MeetSemilattice_540
v0
  = (T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_460 ((T_MeetSemilattice_540 -> T_IsMeetSemilattice_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_540 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_566 (T_MeetSemilattice_540 -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_540
v0))
-- Relation.Binary.Lattice.MeetSemilattice._.isEquivalence
d_isEquivalence_574 ::
  T_MeetSemilattice_540 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_574 :: T_MeetSemilattice_540 -> T_IsEquivalence_26
d_isEquivalence_574 T_MeetSemilattice_540
v0
  = (T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsMeetSemilattice_438 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 ((T_MeetSemilattice_540 -> T_IsMeetSemilattice_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_540 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_566 (T_MeetSemilattice_540 -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_540
v0))))
-- Relation.Binary.Lattice.MeetSemilattice._.isPartialOrder
d_isPartialOrder_576 ::
  T_MeetSemilattice_540 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_162
d_isPartialOrder_576 :: T_MeetSemilattice_540 -> T_IsPartialOrder_162
d_isPartialOrder_576 T_MeetSemilattice_540
v0
  = (T_IsMeetSemilattice_438 -> T_IsPartialOrder_162)
-> AgdaAny -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 ((T_MeetSemilattice_540 -> T_IsMeetSemilattice_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_540 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_566 (T_MeetSemilattice_540 -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_540
v0))
-- Relation.Binary.Lattice.MeetSemilattice._.isPreorder
d_isPreorder_578 ::
  T_MeetSemilattice_540 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_578 :: T_MeetSemilattice_540 -> T_IsPreorder_70
d_isPreorder_578 T_MeetSemilattice_540
v0
  = (T_IsPartialOrder_162 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
      ((T_IsMeetSemilattice_438 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 ((T_MeetSemilattice_540 -> T_IsMeetSemilattice_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_540 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_566 (T_MeetSemilattice_540 -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_540
v0)))
-- Relation.Binary.Lattice.MeetSemilattice._.refl
d_refl_580 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_540 -> AgdaAny -> AgdaAny
d_refl_580 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_MeetSemilattice_540
-> AgdaAny
-> AgdaAny
d_refl_580 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_MeetSemilattice_540
v3 = T_MeetSemilattice_540 -> AgdaAny -> AgdaAny
du_refl_580 T_MeetSemilattice_540
v3
du_refl_580 :: T_MeetSemilattice_540 -> AgdaAny -> AgdaAny
du_refl_580 :: T_MeetSemilattice_540 -> AgdaAny -> AgdaAny
du_refl_580 T_MeetSemilattice_540
v0
  = let v1 :: T_IsMeetSemilattice_438
v1 = T_MeetSemilattice_540 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_566 (T_MeetSemilattice_540 -> T_MeetSemilattice_540
forall a b. a -> b
coe T_MeetSemilattice_540
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 (T_IsMeetSemilattice_438 -> T_IsMeetSemilattice_438
forall a b. a -> b
coe T_IsMeetSemilattice_438
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_70 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_98
            ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
               (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v2))))
-- Relation.Binary.Lattice.MeetSemilattice._.reflexive
d_reflexive_582 ::
  T_MeetSemilattice_540 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_582 :: T_MeetSemilattice_540 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_582 T_MeetSemilattice_540
v0
  = (T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsMeetSemilattice_438 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 ((T_MeetSemilattice_540 -> T_IsMeetSemilattice_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_540 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_566 (T_MeetSemilattice_540 -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_540
v0))))
-- Relation.Binary.Lattice.MeetSemilattice._.trans
d_trans_584 ::
  T_MeetSemilattice_540 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_584 :: T_MeetSemilattice_540
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_584 T_MeetSemilattice_540
v0
  = (T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsMeetSemilattice_438 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 ((T_MeetSemilattice_540 -> T_IsMeetSemilattice_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_540 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_566 (T_MeetSemilattice_540 -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_540
v0))))
-- Relation.Binary.Lattice.MeetSemilattice._.x∧y≤x
d_x'8743'y'8804'x_586 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_540 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'x_586 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_MeetSemilattice_540
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'x_586 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_MeetSemilattice_540
v3 = T_MeetSemilattice_540 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_586 T_MeetSemilattice_540
v3
du_x'8743'y'8804'x_586 ::
  T_MeetSemilattice_540 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_586 :: T_MeetSemilattice_540 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_586 T_MeetSemilattice_540
v0
  = (T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_466 ((T_MeetSemilattice_540 -> T_IsMeetSemilattice_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_540 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_566 (T_MeetSemilattice_540 -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_540
v0))
-- Relation.Binary.Lattice.MeetSemilattice._.x∧y≤y
d_x'8743'y'8804'y_588 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_540 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'y_588 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_MeetSemilattice_540
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'y_588 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_MeetSemilattice_540
v3 = T_MeetSemilattice_540 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_588 T_MeetSemilattice_540
v3
du_x'8743'y'8804'y_588 ::
  T_MeetSemilattice_540 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_588 :: T_MeetSemilattice_540 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_588 T_MeetSemilattice_540
v0
  = (T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_478 ((T_MeetSemilattice_540 -> T_IsMeetSemilattice_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_540 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_566 (T_MeetSemilattice_540 -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_540
v0))
-- Relation.Binary.Lattice.MeetSemilattice._.∧-greatest
d_'8743''45'greatest_590 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_540 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'greatest_590 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_MeetSemilattice_540
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'greatest_590 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_MeetSemilattice_540
v3
  = T_MeetSemilattice_540
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_590 T_MeetSemilattice_540
v3
du_'8743''45'greatest_590 ::
  T_MeetSemilattice_540 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_590 :: T_MeetSemilattice_540
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_590 T_MeetSemilattice_540
v0
  = (T_IsMeetSemilattice_438
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMeetSemilattice_438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_492 ((T_MeetSemilattice_540 -> T_IsMeetSemilattice_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_540 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_566 (T_MeetSemilattice_540 -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_540
v0))
-- Relation.Binary.Lattice.MeetSemilattice._.∼-resp-≈
d_'8764''45'resp'45''8776'_592 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_540 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_592 :: T_Level_18
-> T_Level_18 -> T_Level_18 -> T_MeetSemilattice_540 -> T_Σ_14
d_'8764''45'resp'45''8776'_592 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_MeetSemilattice_540
v3
  = T_MeetSemilattice_540 -> T_Σ_14
du_'8764''45'resp'45''8776'_592 T_MeetSemilattice_540
v3
du_'8764''45'resp'45''8776'_592 ::
  T_MeetSemilattice_540 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_592 :: T_MeetSemilattice_540 -> T_Σ_14
du_'8764''45'resp'45''8776'_592 T_MeetSemilattice_540
v0
  = let v1 :: T_IsMeetSemilattice_438
v1 = T_MeetSemilattice_540 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_566 (T_MeetSemilattice_540 -> T_MeetSemilattice_540
forall a b. a -> b
coe T_MeetSemilattice_540
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 (T_IsMeetSemilattice_438 -> T_IsMeetSemilattice_438
forall a b. a -> b
coe T_IsMeetSemilattice_438
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_70 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_112
            ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
               (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v2))))
-- Relation.Binary.Lattice.MeetSemilattice._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_594 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_540 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_594 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_MeetSemilattice_540
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_594 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_MeetSemilattice_540
v3
  = T_MeetSemilattice_540
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_594 T_MeetSemilattice_540
v3
du_'8764''45'resp'691''45''8776'_594 ::
  T_MeetSemilattice_540 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_594 :: T_MeetSemilattice_540
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_594 T_MeetSemilattice_540
v0
  = let v1 :: T_IsMeetSemilattice_438
v1 = T_MeetSemilattice_540 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_566 (T_MeetSemilattice_540 -> T_MeetSemilattice_540
forall a b. a -> b
coe T_MeetSemilattice_540
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 (T_IsMeetSemilattice_438 -> T_IsMeetSemilattice_438
forall a b. a -> b
coe T_IsMeetSemilattice_438
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_106
            ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
               (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v2))))
-- Relation.Binary.Lattice.MeetSemilattice._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_596 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_540 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_596 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_MeetSemilattice_540
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_596 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_MeetSemilattice_540
v3
  = T_MeetSemilattice_540
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_596 T_MeetSemilattice_540
v3
du_'8764''45'resp'737''45''8776'_596 ::
  T_MeetSemilattice_540 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_596 :: T_MeetSemilattice_540
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_596 T_MeetSemilattice_540
v0
  = let v1 :: T_IsMeetSemilattice_438
v1 = T_MeetSemilattice_540 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_566 (T_MeetSemilattice_540 -> T_MeetSemilattice_540
forall a b. a -> b
coe T_MeetSemilattice_540
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 (T_IsMeetSemilattice_438 -> T_IsMeetSemilattice_438
forall a b. a -> b
coe T_IsMeetSemilattice_438
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_100
            ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
               (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v2))))
-- Relation.Binary.Lattice.MeetSemilattice._.Eq.isPartialEquivalence
d_isPartialEquivalence_600 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_540 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_600 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_MeetSemilattice_540
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_600 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_MeetSemilattice_540
v3
  = T_MeetSemilattice_540 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_600 T_MeetSemilattice_540
v3
du_isPartialEquivalence_600 ::
  T_MeetSemilattice_540 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_600 :: T_MeetSemilattice_540 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_600 T_MeetSemilattice_540
v0
  = let v1 :: T_IsMeetSemilattice_438
v1 = T_MeetSemilattice_540 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_566 (T_MeetSemilattice_540 -> T_MeetSemilattice_540
forall a b. a -> b
coe T_MeetSemilattice_540
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 (T_IsMeetSemilattice_438 -> T_IsMeetSemilattice_438
forall a b. a -> b
coe T_IsMeetSemilattice_438
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreorder_70
v3
                = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                    (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                  (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v3)))))
-- Relation.Binary.Lattice.MeetSemilattice._.Eq.refl
d_refl_602 :: T_MeetSemilattice_540 -> AgdaAny -> AgdaAny
d_refl_602 :: T_MeetSemilattice_540 -> AgdaAny -> AgdaAny
d_refl_602 T_MeetSemilattice_540
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsMeetSemilattice_438 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 ((T_MeetSemilattice_540 -> T_IsMeetSemilattice_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_540 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_566 (T_MeetSemilattice_540 -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_540
v0)))))
-- Relation.Binary.Lattice.MeetSemilattice._.Eq.reflexive
d_reflexive_604 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_540 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_604 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_MeetSemilattice_540
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_604 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_MeetSemilattice_540
v3 = T_MeetSemilattice_540
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_604 T_MeetSemilattice_540
v3
du_reflexive_604 ::
  T_MeetSemilattice_540 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_604 :: T_MeetSemilattice_540
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_604 T_MeetSemilattice_540
v0
  = let v1 :: T_IsMeetSemilattice_438
v1 = T_MeetSemilattice_540 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_566 (T_MeetSemilattice_540 -> T_MeetSemilattice_540
forall a b. a -> b
coe T_MeetSemilattice_540
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 (T_IsMeetSemilattice_438 -> T_IsMeetSemilattice_438
forall a b. a -> b
coe T_IsMeetSemilattice_438
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreorder_70
v3
                = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                    (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                    (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v3))
                 AgdaAny
v4)))
-- Relation.Binary.Lattice.MeetSemilattice._.Eq.sym
d_sym_606 ::
  T_MeetSemilattice_540 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_606 :: T_MeetSemilattice_540 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_606 T_MeetSemilattice_540
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsMeetSemilattice_438 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 ((T_MeetSemilattice_540 -> T_IsMeetSemilattice_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_540 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_566 (T_MeetSemilattice_540 -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_540
v0)))))
-- Relation.Binary.Lattice.MeetSemilattice._.Eq.trans
d_trans_608 ::
  T_MeetSemilattice_540 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_608 :: T_MeetSemilattice_540
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_608 T_MeetSemilattice_540
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsMeetSemilattice_438 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 ((T_MeetSemilattice_540 -> T_IsMeetSemilattice_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_540 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_566 (T_MeetSemilattice_540 -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_540
v0)))))
-- Relation.Binary.Lattice.MeetSemilattice.poset
d_poset_610 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_540 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Poset_282
d_poset_610 :: T_Level_18
-> T_Level_18 -> T_Level_18 -> T_MeetSemilattice_540 -> T_Poset_282
d_poset_610 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_MeetSemilattice_540
v3 = T_MeetSemilattice_540 -> T_Poset_282
du_poset_610 T_MeetSemilattice_540
v3
du_poset_610 ::
  T_MeetSemilattice_540 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Poset_282
du_poset_610 :: T_MeetSemilattice_540 -> T_Poset_282
du_poset_610 T_MeetSemilattice_540
v0
  = (T_IsPartialOrder_162 -> T_Poset_282)
-> T_IsPartialOrder_162 -> T_Poset_282
forall a b. a -> b
coe
      T_IsPartialOrder_162 -> T_Poset_282
MAlonzo.Code.Relation.Binary.Bundles.C_Poset'46'constructor_5219
      (T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 ((T_MeetSemilattice_540 -> T_IsMeetSemilattice_438)
-> AgdaAny -> T_IsMeetSemilattice_438
forall a b. a -> b
coe T_MeetSemilattice_540 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_566 (T_MeetSemilattice_540 -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_540
v0)))
-- Relation.Binary.Lattice.MeetSemilattice._.preorder
d_preorder_614 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_MeetSemilattice_540 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Preorder_132
d_preorder_614 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_MeetSemilattice_540
-> T_Preorder_132
d_preorder_614 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_MeetSemilattice_540
v3 = T_MeetSemilattice_540 -> T_Preorder_132
du_preorder_614 T_MeetSemilattice_540
v3
du_preorder_614 ::
  T_MeetSemilattice_540 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Preorder_132
du_preorder_614 :: T_MeetSemilattice_540 -> T_Preorder_132
du_preorder_614 T_MeetSemilattice_540
v0
  = (T_Poset_282 -> T_Preorder_132) -> AgdaAny -> T_Preorder_132
forall a b. a -> b
coe
      T_Poset_282 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_326
      ((T_MeetSemilattice_540 -> T_Poset_282) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_540 -> T_Poset_282
du_poset_610 (T_MeetSemilattice_540 -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_540
v0))
-- Relation.Binary.Lattice.IsBoundedMeetSemilattice
d_IsBoundedMeetSemilattice_632 :: p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsBoundedMeetSemilattice_632 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 = ()
data T_IsBoundedMeetSemilattice_632
  = C_IsBoundedMeetSemilattice'46'constructor_20757 T_IsMeetSemilattice_438
                                                    (AgdaAny -> AgdaAny)
-- Relation.Binary.Lattice.IsBoundedMeetSemilattice.isMeetSemilattice
d_isMeetSemilattice_654 ::
  T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654 :: T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654 T_IsBoundedMeetSemilattice_632
v0
  = case T_IsBoundedMeetSemilattice_632 -> T_IsBoundedMeetSemilattice_632
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632
v0 of
      C_IsBoundedMeetSemilattice'46'constructor_20757 T_IsMeetSemilattice_438
v1 AgdaAny -> AgdaAny
v2 -> T_IsMeetSemilattice_438 -> T_IsMeetSemilattice_438
forall a b. a -> b
coe T_IsMeetSemilattice_438
v1
      T_IsBoundedMeetSemilattice_632
_ -> T_IsMeetSemilattice_438
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.IsBoundedMeetSemilattice.maximum
d_maximum_656 ::
  T_IsBoundedMeetSemilattice_632 -> AgdaAny -> AgdaAny
d_maximum_656 :: T_IsBoundedMeetSemilattice_632 -> AgdaAny -> AgdaAny
d_maximum_656 T_IsBoundedMeetSemilattice_632
v0
  = case T_IsBoundedMeetSemilattice_632 -> T_IsBoundedMeetSemilattice_632
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632
v0 of
      C_IsBoundedMeetSemilattice'46'constructor_20757 T_IsMeetSemilattice_438
v1 AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_IsBoundedMeetSemilattice_632
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.IsBoundedMeetSemilattice._.antisym
d_antisym_660 ::
  T_IsBoundedMeetSemilattice_632 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_660 :: T_IsBoundedMeetSemilattice_632
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_660 T_IsBoundedMeetSemilattice_632
v0
  = (T_IsPartialOrder_162
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_162
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_172
      ((T_IsMeetSemilattice_438 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 ((T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654 (T_IsBoundedMeetSemilattice_632 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632
v0)))
-- Relation.Binary.Lattice.IsBoundedMeetSemilattice._.infimum
d_infimum_662 ::
  T_IsBoundedMeetSemilattice_632 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_infimum_662 :: T_IsBoundedMeetSemilattice_632 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_662 T_IsBoundedMeetSemilattice_632
v0
  = (T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_460 ((T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654 (T_IsBoundedMeetSemilattice_632 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632
v0))
-- Relation.Binary.Lattice.IsBoundedMeetSemilattice._.isEquivalence
d_isEquivalence_664 ::
  T_IsBoundedMeetSemilattice_632 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_664 :: T_IsBoundedMeetSemilattice_632 -> T_IsEquivalence_26
d_isEquivalence_664 T_IsBoundedMeetSemilattice_632
v0
  = (T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsMeetSemilattice_438 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 ((T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654 (T_IsBoundedMeetSemilattice_632 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632
v0))))
-- Relation.Binary.Lattice.IsBoundedMeetSemilattice._.isPartialOrder
d_isPartialOrder_666 ::
  T_IsBoundedMeetSemilattice_632 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_162
d_isPartialOrder_666 :: T_IsBoundedMeetSemilattice_632 -> T_IsPartialOrder_162
d_isPartialOrder_666 T_IsBoundedMeetSemilattice_632
v0
  = (T_IsMeetSemilattice_438 -> T_IsPartialOrder_162)
-> AgdaAny -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 ((T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654 (T_IsBoundedMeetSemilattice_632 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632
v0))
-- Relation.Binary.Lattice.IsBoundedMeetSemilattice._.isPreorder
d_isPreorder_668 ::
  T_IsBoundedMeetSemilattice_632 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_668 :: T_IsBoundedMeetSemilattice_632 -> T_IsPreorder_70
d_isPreorder_668 T_IsBoundedMeetSemilattice_632
v0
  = (T_IsPartialOrder_162 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
      ((T_IsMeetSemilattice_438 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 ((T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654 (T_IsBoundedMeetSemilattice_632 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632
v0)))
-- Relation.Binary.Lattice.IsBoundedMeetSemilattice._.refl
d_refl_670 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> T_IsBoundedMeetSemilattice_632 -> AgdaAny -> AgdaAny
d_refl_670 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedMeetSemilattice_632
-> AgdaAny
-> AgdaAny
d_refl_670 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedMeetSemilattice_632
v8 = T_IsBoundedMeetSemilattice_632 -> AgdaAny -> AgdaAny
du_refl_670 T_IsBoundedMeetSemilattice_632
v8
du_refl_670 :: T_IsBoundedMeetSemilattice_632 -> AgdaAny -> AgdaAny
du_refl_670 :: T_IsBoundedMeetSemilattice_632 -> AgdaAny -> AgdaAny
du_refl_670 T_IsBoundedMeetSemilattice_632
v0
  = let v1 :: T_IsMeetSemilattice_438
v1 = T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654 (T_IsBoundedMeetSemilattice_632 -> T_IsBoundedMeetSemilattice_632
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 (T_IsMeetSemilattice_438 -> T_IsMeetSemilattice_438
forall a b. a -> b
coe T_IsMeetSemilattice_438
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_70 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_98
            ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
               (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v2))))
-- Relation.Binary.Lattice.IsBoundedMeetSemilattice._.reflexive
d_reflexive_672 ::
  T_IsBoundedMeetSemilattice_632 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_672 :: T_IsBoundedMeetSemilattice_632
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_672 T_IsBoundedMeetSemilattice_632
v0
  = (T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsMeetSemilattice_438 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 ((T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654 (T_IsBoundedMeetSemilattice_632 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632
v0))))
-- Relation.Binary.Lattice.IsBoundedMeetSemilattice._.trans
d_trans_674 ::
  T_IsBoundedMeetSemilattice_632 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_674 :: T_IsBoundedMeetSemilattice_632
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_674 T_IsBoundedMeetSemilattice_632
v0
  = (T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsMeetSemilattice_438 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 ((T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654 (T_IsBoundedMeetSemilattice_632 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632
v0))))
-- Relation.Binary.Lattice.IsBoundedMeetSemilattice._.x∧y≤x
d_x'8743'y'8804'x_676 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsBoundedMeetSemilattice_632 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'x_676 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedMeetSemilattice_632
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'x_676 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedMeetSemilattice_632
v8
  = T_IsBoundedMeetSemilattice_632 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_676 T_IsBoundedMeetSemilattice_632
v8
du_x'8743'y'8804'x_676 ::
  T_IsBoundedMeetSemilattice_632 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_676 :: T_IsBoundedMeetSemilattice_632 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_676 T_IsBoundedMeetSemilattice_632
v0
  = (T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_466 ((T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654 (T_IsBoundedMeetSemilattice_632 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632
v0))
-- Relation.Binary.Lattice.IsBoundedMeetSemilattice._.x∧y≤y
d_x'8743'y'8804'y_678 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsBoundedMeetSemilattice_632 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'y_678 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedMeetSemilattice_632
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'y_678 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedMeetSemilattice_632
v8
  = T_IsBoundedMeetSemilattice_632 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_678 T_IsBoundedMeetSemilattice_632
v8
du_x'8743'y'8804'y_678 ::
  T_IsBoundedMeetSemilattice_632 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_678 :: T_IsBoundedMeetSemilattice_632 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_678 T_IsBoundedMeetSemilattice_632
v0
  = (T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_478 ((T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654 (T_IsBoundedMeetSemilattice_632 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632
v0))
-- Relation.Binary.Lattice.IsBoundedMeetSemilattice._.∧-greatest
d_'8743''45'greatest_680 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsBoundedMeetSemilattice_632 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'greatest_680 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedMeetSemilattice_632
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'greatest_680 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedMeetSemilattice_632
v8
  = T_IsBoundedMeetSemilattice_632
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_680 T_IsBoundedMeetSemilattice_632
v8
du_'8743''45'greatest_680 ::
  T_IsBoundedMeetSemilattice_632 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_680 :: T_IsBoundedMeetSemilattice_632
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_680 T_IsBoundedMeetSemilattice_632
v0
  = (T_IsMeetSemilattice_438
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMeetSemilattice_438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_492 ((T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654 (T_IsBoundedMeetSemilattice_632 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632
v0))
-- Relation.Binary.Lattice.IsBoundedMeetSemilattice._.∼-resp-≈
d_'8764''45'resp'45''8776'_682 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsBoundedMeetSemilattice_632 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_682 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedMeetSemilattice_632
-> T_Σ_14
d_'8764''45'resp'45''8776'_682 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedMeetSemilattice_632
v8
  = T_IsBoundedMeetSemilattice_632 -> T_Σ_14
du_'8764''45'resp'45''8776'_682 T_IsBoundedMeetSemilattice_632
v8
du_'8764''45'resp'45''8776'_682 ::
  T_IsBoundedMeetSemilattice_632 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_682 :: T_IsBoundedMeetSemilattice_632 -> T_Σ_14
du_'8764''45'resp'45''8776'_682 T_IsBoundedMeetSemilattice_632
v0
  = let v1 :: T_IsMeetSemilattice_438
v1 = T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654 (T_IsBoundedMeetSemilattice_632 -> T_IsBoundedMeetSemilattice_632
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 (T_IsMeetSemilattice_438 -> T_IsMeetSemilattice_438
forall a b. a -> b
coe T_IsMeetSemilattice_438
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_70 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_112
            ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
               (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v2))))
-- Relation.Binary.Lattice.IsBoundedMeetSemilattice._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_684 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsBoundedMeetSemilattice_632 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_684 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedMeetSemilattice_632
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_684 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7
                                    T_IsBoundedMeetSemilattice_632
v8
  = T_IsBoundedMeetSemilattice_632
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_684 T_IsBoundedMeetSemilattice_632
v8
du_'8764''45'resp'691''45''8776'_684 ::
  T_IsBoundedMeetSemilattice_632 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_684 :: T_IsBoundedMeetSemilattice_632
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_684 T_IsBoundedMeetSemilattice_632
v0
  = let v1 :: T_IsMeetSemilattice_438
v1 = T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654 (T_IsBoundedMeetSemilattice_632 -> T_IsBoundedMeetSemilattice_632
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 (T_IsMeetSemilattice_438 -> T_IsMeetSemilattice_438
forall a b. a -> b
coe T_IsMeetSemilattice_438
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_106
            ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
               (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v2))))
-- Relation.Binary.Lattice.IsBoundedMeetSemilattice._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_686 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsBoundedMeetSemilattice_632 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_686 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedMeetSemilattice_632
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_686 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7
                                    T_IsBoundedMeetSemilattice_632
v8
  = T_IsBoundedMeetSemilattice_632
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_686 T_IsBoundedMeetSemilattice_632
v8
du_'8764''45'resp'737''45''8776'_686 ::
  T_IsBoundedMeetSemilattice_632 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_686 :: T_IsBoundedMeetSemilattice_632
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_686 T_IsBoundedMeetSemilattice_632
v0
  = let v1 :: T_IsMeetSemilattice_438
v1 = T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654 (T_IsBoundedMeetSemilattice_632 -> T_IsBoundedMeetSemilattice_632
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 (T_IsMeetSemilattice_438 -> T_IsMeetSemilattice_438
forall a b. a -> b
coe T_IsMeetSemilattice_438
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_100
            ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
               (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v2))))
-- Relation.Binary.Lattice.IsBoundedMeetSemilattice._.Eq.isPartialEquivalence
d_isPartialEquivalence_690 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsBoundedMeetSemilattice_632 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_690 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedMeetSemilattice_632
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_690 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedMeetSemilattice_632
v8
  = T_IsBoundedMeetSemilattice_632 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_690 T_IsBoundedMeetSemilattice_632
v8
du_isPartialEquivalence_690 ::
  T_IsBoundedMeetSemilattice_632 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_690 :: T_IsBoundedMeetSemilattice_632 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_690 T_IsBoundedMeetSemilattice_632
v0
  = let v1 :: T_IsMeetSemilattice_438
v1 = T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654 (T_IsBoundedMeetSemilattice_632 -> T_IsBoundedMeetSemilattice_632
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 (T_IsMeetSemilattice_438 -> T_IsMeetSemilattice_438
forall a b. a -> b
coe T_IsMeetSemilattice_438
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreorder_70
v3
                = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                    (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                  (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v3)))))
-- Relation.Binary.Lattice.IsBoundedMeetSemilattice._.Eq.refl
d_refl_692 :: T_IsBoundedMeetSemilattice_632 -> AgdaAny -> AgdaAny
d_refl_692 :: T_IsBoundedMeetSemilattice_632 -> AgdaAny -> AgdaAny
d_refl_692 T_IsBoundedMeetSemilattice_632
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsMeetSemilattice_438 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 ((T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654 (T_IsBoundedMeetSemilattice_632 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632
v0)))))
-- Relation.Binary.Lattice.IsBoundedMeetSemilattice._.Eq.reflexive
d_reflexive_694 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsBoundedMeetSemilattice_632 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_694 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedMeetSemilattice_632
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_694 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedMeetSemilattice_632
v8
  = T_IsBoundedMeetSemilattice_632
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_694 T_IsBoundedMeetSemilattice_632
v8
du_reflexive_694 ::
  T_IsBoundedMeetSemilattice_632 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_694 :: T_IsBoundedMeetSemilattice_632
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_694 T_IsBoundedMeetSemilattice_632
v0
  = let v1 :: T_IsMeetSemilattice_438
v1 = T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654 (T_IsBoundedMeetSemilattice_632 -> T_IsBoundedMeetSemilattice_632
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 (T_IsMeetSemilattice_438 -> T_IsMeetSemilattice_438
forall a b. a -> b
coe T_IsMeetSemilattice_438
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreorder_70
v3
                = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                    (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                    (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v3))
                 AgdaAny
v4)))
-- Relation.Binary.Lattice.IsBoundedMeetSemilattice._.Eq.sym
d_sym_696 ::
  T_IsBoundedMeetSemilattice_632 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_696 :: T_IsBoundedMeetSemilattice_632
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_696 T_IsBoundedMeetSemilattice_632
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsMeetSemilattice_438 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 ((T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654 (T_IsBoundedMeetSemilattice_632 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632
v0)))))
-- Relation.Binary.Lattice.IsBoundedMeetSemilattice._.Eq.trans
d_trans_698 ::
  T_IsBoundedMeetSemilattice_632 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_698 :: T_IsBoundedMeetSemilattice_632
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_698 T_IsBoundedMeetSemilattice_632
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsMeetSemilattice_438 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 ((T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654 (T_IsBoundedMeetSemilattice_632 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632
v0)))))
-- Relation.Binary.Lattice.BoundedMeetSemilattice
d_BoundedMeetSemilattice_706 :: p -> p -> p -> T_Level_18
d_BoundedMeetSemilattice_706 p
a0 p
a1 p
a2 = ()
data T_BoundedMeetSemilattice_706
  = C_BoundedMeetSemilattice'46'constructor_23291 (AgdaAny ->
                                                   AgdaAny -> AgdaAny)
                                                  AgdaAny T_IsBoundedMeetSemilattice_632
-- Relation.Binary.Lattice.BoundedMeetSemilattice.Carrier
d_Carrier_726 :: T_BoundedMeetSemilattice_706 -> ()
d_Carrier_726 :: T_BoundedMeetSemilattice_706 -> T_Level_18
d_Carrier_726 = T_BoundedMeetSemilattice_706 -> T_Level_18
forall a. a
erased
-- Relation.Binary.Lattice.BoundedMeetSemilattice._≈_
d__'8776'__728 ::
  T_BoundedMeetSemilattice_706 -> AgdaAny -> AgdaAny -> ()
d__'8776'__728 :: T_BoundedMeetSemilattice_706 -> AgdaAny -> AgdaAny -> T_Level_18
d__'8776'__728 = T_BoundedMeetSemilattice_706 -> AgdaAny -> AgdaAny -> T_Level_18
forall a. a
erased
-- Relation.Binary.Lattice.BoundedMeetSemilattice._≤_
d__'8804'__730 ::
  T_BoundedMeetSemilattice_706 -> AgdaAny -> AgdaAny -> ()
d__'8804'__730 :: T_BoundedMeetSemilattice_706 -> AgdaAny -> AgdaAny -> T_Level_18
d__'8804'__730 = T_BoundedMeetSemilattice_706 -> AgdaAny -> AgdaAny -> T_Level_18
forall a. a
erased
-- Relation.Binary.Lattice.BoundedMeetSemilattice._∧_
d__'8743'__732 ::
  T_BoundedMeetSemilattice_706 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__732 :: T_BoundedMeetSemilattice_706 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__732 T_BoundedMeetSemilattice_706
v0
  = case T_BoundedMeetSemilattice_706 -> T_BoundedMeetSemilattice_706
forall a b. a -> b
coe T_BoundedMeetSemilattice_706
v0 of
      C_BoundedMeetSemilattice'46'constructor_23291 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 T_IsBoundedMeetSemilattice_632
v6 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_BoundedMeetSemilattice_706
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.BoundedMeetSemilattice.⊤
d_'8868'_734 :: T_BoundedMeetSemilattice_706 -> AgdaAny
d_'8868'_734 :: T_BoundedMeetSemilattice_706 -> AgdaAny
d_'8868'_734 T_BoundedMeetSemilattice_706
v0
  = case T_BoundedMeetSemilattice_706 -> T_BoundedMeetSemilattice_706
forall a b. a -> b
coe T_BoundedMeetSemilattice_706
v0 of
      C_BoundedMeetSemilattice'46'constructor_23291 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 T_IsBoundedMeetSemilattice_632
v6 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5
      T_BoundedMeetSemilattice_706
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.BoundedMeetSemilattice.isBoundedMeetSemilattice
d_isBoundedMeetSemilattice_736 ::
  T_BoundedMeetSemilattice_706 -> T_IsBoundedMeetSemilattice_632
d_isBoundedMeetSemilattice_736 :: T_BoundedMeetSemilattice_706 -> T_IsBoundedMeetSemilattice_632
d_isBoundedMeetSemilattice_736 T_BoundedMeetSemilattice_706
v0
  = case T_BoundedMeetSemilattice_706 -> T_BoundedMeetSemilattice_706
forall a b. a -> b
coe T_BoundedMeetSemilattice_706
v0 of
      C_BoundedMeetSemilattice'46'constructor_23291 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 T_IsBoundedMeetSemilattice_632
v6 -> T_IsBoundedMeetSemilattice_632 -> T_IsBoundedMeetSemilattice_632
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632
v6
      T_BoundedMeetSemilattice_706
_ -> T_IsBoundedMeetSemilattice_632
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.BoundedMeetSemilattice._.antisym
d_antisym_740 ::
  T_BoundedMeetSemilattice_706 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_740 :: T_BoundedMeetSemilattice_706
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_740 T_BoundedMeetSemilattice_706
v0
  = (T_IsPartialOrder_162
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_162
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_172
      ((T_IsMeetSemilattice_438 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458
         ((T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654
            ((T_BoundedMeetSemilattice_706 -> T_IsBoundedMeetSemilattice_632)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_706 -> T_IsBoundedMeetSemilattice_632
d_isBoundedMeetSemilattice_736 (T_BoundedMeetSemilattice_706 -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_706
v0))))
-- Relation.Binary.Lattice.BoundedMeetSemilattice._.infimum
d_infimum_742 ::
  T_BoundedMeetSemilattice_706 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_infimum_742 :: T_BoundedMeetSemilattice_706 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_742 T_BoundedMeetSemilattice_706
v0
  = (T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_460
      ((T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654
         ((T_BoundedMeetSemilattice_706 -> T_IsBoundedMeetSemilattice_632)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_706 -> T_IsBoundedMeetSemilattice_632
d_isBoundedMeetSemilattice_736 (T_BoundedMeetSemilattice_706 -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_706
v0)))
-- Relation.Binary.Lattice.BoundedMeetSemilattice._.isEquivalence
d_isEquivalence_744 ::
  T_BoundedMeetSemilattice_706 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_744 :: T_BoundedMeetSemilattice_706 -> T_IsEquivalence_26
d_isEquivalence_744 T_BoundedMeetSemilattice_706
v0
  = (T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsMeetSemilattice_438 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458
            ((T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654
               ((T_BoundedMeetSemilattice_706 -> T_IsBoundedMeetSemilattice_632)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_706 -> T_IsBoundedMeetSemilattice_632
d_isBoundedMeetSemilattice_736 (T_BoundedMeetSemilattice_706 -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_706
v0)))))
-- Relation.Binary.Lattice.BoundedMeetSemilattice._.isMeetSemilattice
d_isMeetSemilattice_746 ::
  T_BoundedMeetSemilattice_706 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_746 :: T_BoundedMeetSemilattice_706 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_746 T_BoundedMeetSemilattice_706
v0
  = (T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438)
-> AgdaAny -> T_IsMeetSemilattice_438
forall a b. a -> b
coe
      T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654
      ((T_BoundedMeetSemilattice_706 -> T_IsBoundedMeetSemilattice_632)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_706 -> T_IsBoundedMeetSemilattice_632
d_isBoundedMeetSemilattice_736 (T_BoundedMeetSemilattice_706 -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_706
v0))
-- Relation.Binary.Lattice.BoundedMeetSemilattice._.isPartialOrder
d_isPartialOrder_748 ::
  T_BoundedMeetSemilattice_706 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_162
d_isPartialOrder_748 :: T_BoundedMeetSemilattice_706 -> T_IsPartialOrder_162
d_isPartialOrder_748 T_BoundedMeetSemilattice_706
v0
  = (T_IsMeetSemilattice_438 -> T_IsPartialOrder_162)
-> AgdaAny -> T_IsPartialOrder_162
forall a b. a -> b
coe
      T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458
      ((T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654
         ((T_BoundedMeetSemilattice_706 -> T_IsBoundedMeetSemilattice_632)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_706 -> T_IsBoundedMeetSemilattice_632
d_isBoundedMeetSemilattice_736 (T_BoundedMeetSemilattice_706 -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_706
v0)))
-- Relation.Binary.Lattice.BoundedMeetSemilattice._.isPreorder
d_isPreorder_750 ::
  T_BoundedMeetSemilattice_706 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_750 :: T_BoundedMeetSemilattice_706 -> T_IsPreorder_70
d_isPreorder_750 T_BoundedMeetSemilattice_706
v0
  = (T_IsPartialOrder_162 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
      ((T_IsMeetSemilattice_438 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458
         ((T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654
            ((T_BoundedMeetSemilattice_706 -> T_IsBoundedMeetSemilattice_632)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_706 -> T_IsBoundedMeetSemilattice_632
d_isBoundedMeetSemilattice_736 (T_BoundedMeetSemilattice_706 -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_706
v0))))
-- Relation.Binary.Lattice.BoundedMeetSemilattice._.maximum
d_maximum_752 :: T_BoundedMeetSemilattice_706 -> AgdaAny -> AgdaAny
d_maximum_752 :: T_BoundedMeetSemilattice_706 -> AgdaAny -> AgdaAny
d_maximum_752 T_BoundedMeetSemilattice_706
v0
  = (T_IsBoundedMeetSemilattice_632 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632 -> AgdaAny -> AgdaAny
d_maximum_656 ((T_BoundedMeetSemilattice_706 -> T_IsBoundedMeetSemilattice_632)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_706 -> T_IsBoundedMeetSemilattice_632
d_isBoundedMeetSemilattice_736 (T_BoundedMeetSemilattice_706 -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_706
v0))
-- Relation.Binary.Lattice.BoundedMeetSemilattice._.refl
d_refl_754 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_706 -> AgdaAny -> AgdaAny
d_refl_754 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedMeetSemilattice_706
-> AgdaAny
-> AgdaAny
d_refl_754 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedMeetSemilattice_706
v3 = T_BoundedMeetSemilattice_706 -> AgdaAny -> AgdaAny
du_refl_754 T_BoundedMeetSemilattice_706
v3
du_refl_754 :: T_BoundedMeetSemilattice_706 -> AgdaAny -> AgdaAny
du_refl_754 :: T_BoundedMeetSemilattice_706 -> AgdaAny -> AgdaAny
du_refl_754 T_BoundedMeetSemilattice_706
v0
  = let v1 :: T_IsBoundedMeetSemilattice_632
v1 = T_BoundedMeetSemilattice_706 -> T_IsBoundedMeetSemilattice_632
d_isBoundedMeetSemilattice_736 (T_BoundedMeetSemilattice_706 -> T_BoundedMeetSemilattice_706
forall a b. a -> b
coe T_BoundedMeetSemilattice_706
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMeetSemilattice_438
v2 = T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654 (T_IsBoundedMeetSemilattice_632 -> T_IsBoundedMeetSemilattice_632
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3 = T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 (T_IsMeetSemilattice_438 -> T_IsMeetSemilattice_438
forall a b. a -> b
coe T_IsMeetSemilattice_438
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsPreorder_70 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_70 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_98
               ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                  (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v3)))))
-- Relation.Binary.Lattice.BoundedMeetSemilattice._.reflexive
d_reflexive_756 ::
  T_BoundedMeetSemilattice_706 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_756 :: T_BoundedMeetSemilattice_706
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_756 T_BoundedMeetSemilattice_706
v0
  = (T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsMeetSemilattice_438 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458
            ((T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654
               ((T_BoundedMeetSemilattice_706 -> T_IsBoundedMeetSemilattice_632)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_706 -> T_IsBoundedMeetSemilattice_632
d_isBoundedMeetSemilattice_736 (T_BoundedMeetSemilattice_706 -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_706
v0)))))
-- Relation.Binary.Lattice.BoundedMeetSemilattice._.trans
d_trans_758 ::
  T_BoundedMeetSemilattice_706 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_758 :: T_BoundedMeetSemilattice_706
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_758 T_BoundedMeetSemilattice_706
v0
  = (T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsMeetSemilattice_438 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458
            ((T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654
               ((T_BoundedMeetSemilattice_706 -> T_IsBoundedMeetSemilattice_632)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_706 -> T_IsBoundedMeetSemilattice_632
d_isBoundedMeetSemilattice_736 (T_BoundedMeetSemilattice_706 -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_706
v0)))))
-- Relation.Binary.Lattice.BoundedMeetSemilattice._.x∧y≤x
d_x'8743'y'8804'x_760 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_706 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'x_760 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedMeetSemilattice_706
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'x_760 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedMeetSemilattice_706
v3 = T_BoundedMeetSemilattice_706 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_760 T_BoundedMeetSemilattice_706
v3
du_x'8743'y'8804'x_760 ::
  T_BoundedMeetSemilattice_706 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_760 :: T_BoundedMeetSemilattice_706 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_760 T_BoundedMeetSemilattice_706
v0
  = let v1 :: T_IsBoundedMeetSemilattice_632
v1 = T_BoundedMeetSemilattice_706 -> T_IsBoundedMeetSemilattice_632
d_isBoundedMeetSemilattice_736 (T_BoundedMeetSemilattice_706 -> T_BoundedMeetSemilattice_706
forall a b. a -> b
coe T_BoundedMeetSemilattice_706
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_466 ((T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654 (T_IsBoundedMeetSemilattice_632 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632
v1)))
-- Relation.Binary.Lattice.BoundedMeetSemilattice._.x∧y≤y
d_x'8743'y'8804'y_762 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_706 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'y_762 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedMeetSemilattice_706
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'y_762 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedMeetSemilattice_706
v3 = T_BoundedMeetSemilattice_706 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_762 T_BoundedMeetSemilattice_706
v3
du_x'8743'y'8804'y_762 ::
  T_BoundedMeetSemilattice_706 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_762 :: T_BoundedMeetSemilattice_706 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_762 T_BoundedMeetSemilattice_706
v0
  = let v1 :: T_IsBoundedMeetSemilattice_632
v1 = T_BoundedMeetSemilattice_706 -> T_IsBoundedMeetSemilattice_632
d_isBoundedMeetSemilattice_736 (T_BoundedMeetSemilattice_706 -> T_BoundedMeetSemilattice_706
forall a b. a -> b
coe T_BoundedMeetSemilattice_706
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_478 ((T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654 (T_IsBoundedMeetSemilattice_632 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632
v1)))
-- Relation.Binary.Lattice.BoundedMeetSemilattice._.∧-greatest
d_'8743''45'greatest_764 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_706 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'greatest_764 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedMeetSemilattice_706
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'greatest_764 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedMeetSemilattice_706
v3
  = T_BoundedMeetSemilattice_706
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_764 T_BoundedMeetSemilattice_706
v3
du_'8743''45'greatest_764 ::
  T_BoundedMeetSemilattice_706 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_764 :: T_BoundedMeetSemilattice_706
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_764 T_BoundedMeetSemilattice_706
v0
  = let v1 :: T_IsBoundedMeetSemilattice_632
v1 = T_BoundedMeetSemilattice_706 -> T_IsBoundedMeetSemilattice_632
d_isBoundedMeetSemilattice_736 (T_BoundedMeetSemilattice_706 -> T_BoundedMeetSemilattice_706
forall a b. a -> b
coe T_BoundedMeetSemilattice_706
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMeetSemilattice_438
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMeetSemilattice_438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_492 ((T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654 (T_IsBoundedMeetSemilattice_632 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632
v1)))
-- Relation.Binary.Lattice.BoundedMeetSemilattice._.∼-resp-≈
d_'8764''45'resp'45''8776'_766 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_706 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_766 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedMeetSemilattice_706
-> T_Σ_14
d_'8764''45'resp'45''8776'_766 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedMeetSemilattice_706
v3
  = T_BoundedMeetSemilattice_706 -> T_Σ_14
du_'8764''45'resp'45''8776'_766 T_BoundedMeetSemilattice_706
v3
du_'8764''45'resp'45''8776'_766 ::
  T_BoundedMeetSemilattice_706 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_766 :: T_BoundedMeetSemilattice_706 -> T_Σ_14
du_'8764''45'resp'45''8776'_766 T_BoundedMeetSemilattice_706
v0
  = let v1 :: T_IsBoundedMeetSemilattice_632
v1 = T_BoundedMeetSemilattice_706 -> T_IsBoundedMeetSemilattice_632
d_isBoundedMeetSemilattice_736 (T_BoundedMeetSemilattice_706 -> T_BoundedMeetSemilattice_706
forall a b. a -> b
coe T_BoundedMeetSemilattice_706
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsMeetSemilattice_438
v2 = T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654 (T_IsBoundedMeetSemilattice_632 -> T_IsBoundedMeetSemilattice_632
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3 = T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 (T_IsMeetSemilattice_438 -> T_IsMeetSemilattice_438
forall a b. a -> b
coe T_IsMeetSemilattice_438
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsPreorder_70 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_70 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_112
               ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                  (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v3)))))
-- Relation.Binary.Lattice.BoundedMeetSemilattice._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_768 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_706 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_768 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedMeetSemilattice_706
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_768 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedMeetSemilattice_706
v3
  = T_BoundedMeetSemilattice_706
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_768 T_BoundedMeetSemilattice_706
v3
du_'8764''45'resp'691''45''8776'_768 ::
  T_BoundedMeetSemilattice_706 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_768 :: T_BoundedMeetSemilattice_706
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_768 T_BoundedMeetSemilattice_706
v0
  = let v1 :: T_IsBoundedMeetSemilattice_632
v1 = T_BoundedMeetSemilattice_706 -> T_IsBoundedMeetSemilattice_632
d_isBoundedMeetSemilattice_736 (T_BoundedMeetSemilattice_706 -> T_BoundedMeetSemilattice_706
forall a b. a -> b
coe T_BoundedMeetSemilattice_706
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMeetSemilattice_438
v2 = T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654 (T_IsBoundedMeetSemilattice_632 -> T_IsBoundedMeetSemilattice_632
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3 = T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 (T_IsMeetSemilattice_438 -> T_IsMeetSemilattice_438
forall a b. a -> b
coe T_IsMeetSemilattice_438
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_106
               ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                  (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v3)))))
-- Relation.Binary.Lattice.BoundedMeetSemilattice._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_770 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_706 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_770 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedMeetSemilattice_706
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_770 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedMeetSemilattice_706
v3
  = T_BoundedMeetSemilattice_706
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_770 T_BoundedMeetSemilattice_706
v3
du_'8764''45'resp'737''45''8776'_770 ::
  T_BoundedMeetSemilattice_706 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_770 :: T_BoundedMeetSemilattice_706
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_770 T_BoundedMeetSemilattice_706
v0
  = let v1 :: T_IsBoundedMeetSemilattice_632
v1 = T_BoundedMeetSemilattice_706 -> T_IsBoundedMeetSemilattice_632
d_isBoundedMeetSemilattice_736 (T_BoundedMeetSemilattice_706 -> T_BoundedMeetSemilattice_706
forall a b. a -> b
coe T_BoundedMeetSemilattice_706
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMeetSemilattice_438
v2 = T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654 (T_IsBoundedMeetSemilattice_632 -> T_IsBoundedMeetSemilattice_632
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3 = T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 (T_IsMeetSemilattice_438 -> T_IsMeetSemilattice_438
forall a b. a -> b
coe T_IsMeetSemilattice_438
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_100
               ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                  (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v3)))))
-- Relation.Binary.Lattice.BoundedMeetSemilattice._.Eq.isPartialEquivalence
d_isPartialEquivalence_774 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_706 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_774 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedMeetSemilattice_706
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_774 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedMeetSemilattice_706
v3
  = T_BoundedMeetSemilattice_706 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_774 T_BoundedMeetSemilattice_706
v3
du_isPartialEquivalence_774 ::
  T_BoundedMeetSemilattice_706 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_774 :: T_BoundedMeetSemilattice_706 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_774 T_BoundedMeetSemilattice_706
v0
  = let v1 :: T_IsBoundedMeetSemilattice_632
v1 = T_BoundedMeetSemilattice_706 -> T_IsBoundedMeetSemilattice_632
d_isBoundedMeetSemilattice_736 (T_BoundedMeetSemilattice_706 -> T_BoundedMeetSemilattice_706
forall a b. a -> b
coe T_BoundedMeetSemilattice_706
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsMeetSemilattice_438
v2 = T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654 (T_IsBoundedMeetSemilattice_632 -> T_IsBoundedMeetSemilattice_632
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3 = T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 (T_IsMeetSemilattice_438 -> T_IsMeetSemilattice_438
forall a b. a -> b
coe T_IsMeetSemilattice_438
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreorder_70
v4
                   = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                       (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                     (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v4))))))
-- Relation.Binary.Lattice.BoundedMeetSemilattice._.Eq.refl
d_refl_776 :: T_BoundedMeetSemilattice_706 -> AgdaAny -> AgdaAny
d_refl_776 :: T_BoundedMeetSemilattice_706 -> AgdaAny -> AgdaAny
d_refl_776 T_BoundedMeetSemilattice_706
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsMeetSemilattice_438 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458
               ((T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654
                  ((T_BoundedMeetSemilattice_706 -> T_IsBoundedMeetSemilattice_632)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_706 -> T_IsBoundedMeetSemilattice_632
d_isBoundedMeetSemilattice_736 (T_BoundedMeetSemilattice_706 -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_706
v0))))))
-- Relation.Binary.Lattice.BoundedMeetSemilattice._.Eq.reflexive
d_reflexive_778 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_706 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_778 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedMeetSemilattice_706
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_778 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedMeetSemilattice_706
v3 = T_BoundedMeetSemilattice_706
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_778 T_BoundedMeetSemilattice_706
v3
du_reflexive_778 ::
  T_BoundedMeetSemilattice_706 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_778 :: T_BoundedMeetSemilattice_706
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_778 T_BoundedMeetSemilattice_706
v0
  = let v1 :: T_IsBoundedMeetSemilattice_632
v1 = T_BoundedMeetSemilattice_706 -> T_IsBoundedMeetSemilattice_632
d_isBoundedMeetSemilattice_736 (T_BoundedMeetSemilattice_706 -> T_BoundedMeetSemilattice_706
forall a b. a -> b
coe T_BoundedMeetSemilattice_706
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsMeetSemilattice_438
v2 = T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654 (T_IsBoundedMeetSemilattice_632 -> T_IsBoundedMeetSemilattice_632
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_632
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3 = T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458 (T_IsMeetSemilattice_438 -> T_IsMeetSemilattice_438
forall a b. a -> b
coe T_IsMeetSemilattice_438
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreorder_70
v4
                   = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                       (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                       (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v4))
                    AgdaAny
v5))))
-- Relation.Binary.Lattice.BoundedMeetSemilattice._.Eq.sym
d_sym_780 ::
  T_BoundedMeetSemilattice_706 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_780 :: T_BoundedMeetSemilattice_706
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_780 T_BoundedMeetSemilattice_706
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsMeetSemilattice_438 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458
               ((T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654
                  ((T_BoundedMeetSemilattice_706 -> T_IsBoundedMeetSemilattice_632)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_706 -> T_IsBoundedMeetSemilattice_632
d_isBoundedMeetSemilattice_736 (T_BoundedMeetSemilattice_706 -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_706
v0))))))
-- Relation.Binary.Lattice.BoundedMeetSemilattice._.Eq.trans
d_trans_782 ::
  T_BoundedMeetSemilattice_706 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_782 :: T_BoundedMeetSemilattice_706
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_782 T_BoundedMeetSemilattice_706
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsMeetSemilattice_438 -> T_IsPartialOrder_162)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMeetSemilattice_438 -> T_IsPartialOrder_162
d_isPartialOrder_458
               ((T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654
                  ((T_BoundedMeetSemilattice_706 -> T_IsBoundedMeetSemilattice_632)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_706 -> T_IsBoundedMeetSemilattice_632
d_isBoundedMeetSemilattice_736 (T_BoundedMeetSemilattice_706 -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_706
v0))))))
-- Relation.Binary.Lattice.BoundedMeetSemilattice.meetSemilattice
d_meetSemilattice_784 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_706 -> T_MeetSemilattice_540
d_meetSemilattice_784 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedMeetSemilattice_706
-> T_MeetSemilattice_540
d_meetSemilattice_784 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedMeetSemilattice_706
v3 = T_BoundedMeetSemilattice_706 -> T_MeetSemilattice_540
du_meetSemilattice_784 T_BoundedMeetSemilattice_706
v3
du_meetSemilattice_784 ::
  T_BoundedMeetSemilattice_706 -> T_MeetSemilattice_540
du_meetSemilattice_784 :: T_BoundedMeetSemilattice_706 -> T_MeetSemilattice_540
du_meetSemilattice_784 T_BoundedMeetSemilattice_706
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsMeetSemilattice_438 -> T_MeetSemilattice_540)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMeetSemilattice_438
-> T_MeetSemilattice_540
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMeetSemilattice_438 -> T_MeetSemilattice_540
C_MeetSemilattice'46'constructor_18685 (T_BoundedMeetSemilattice_706 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__732 (T_BoundedMeetSemilattice_706 -> T_BoundedMeetSemilattice_706
forall a b. a -> b
coe T_BoundedMeetSemilattice_706
v0))
      (T_IsBoundedMeetSemilattice_632 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_654
         ((T_BoundedMeetSemilattice_706 -> T_IsBoundedMeetSemilattice_632)
-> AgdaAny -> T_IsBoundedMeetSemilattice_632
forall a b. a -> b
coe T_BoundedMeetSemilattice_706 -> T_IsBoundedMeetSemilattice_632
d_isBoundedMeetSemilattice_736 (T_BoundedMeetSemilattice_706 -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_706
v0)))
-- Relation.Binary.Lattice.BoundedMeetSemilattice.meetSemiLattice
d_meetSemiLattice_786 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_706 -> T_MeetSemilattice_540
d_meetSemiLattice_786 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedMeetSemilattice_706
-> T_MeetSemilattice_540
d_meetSemiLattice_786 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedMeetSemilattice_706
v3 = T_BoundedMeetSemilattice_706 -> T_MeetSemilattice_540
du_meetSemiLattice_786 T_BoundedMeetSemilattice_706
v3
du_meetSemiLattice_786 ::
  T_BoundedMeetSemilattice_706 -> T_MeetSemilattice_540
du_meetSemiLattice_786 :: T_BoundedMeetSemilattice_706 -> T_MeetSemilattice_540
du_meetSemiLattice_786 T_BoundedMeetSemilattice_706
v0 = (T_BoundedMeetSemilattice_706 -> T_MeetSemilattice_540)
-> AgdaAny -> T_MeetSemilattice_540
forall a b. a -> b
coe T_BoundedMeetSemilattice_706 -> T_MeetSemilattice_540
du_meetSemilattice_784 (T_BoundedMeetSemilattice_706 -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_706
v0)
-- Relation.Binary.Lattice.BoundedMeetSemilattice._.poset
d_poset_790 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_706 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Poset_282
d_poset_790 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedMeetSemilattice_706
-> T_Poset_282
d_poset_790 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedMeetSemilattice_706
v3 = T_BoundedMeetSemilattice_706 -> T_Poset_282
du_poset_790 T_BoundedMeetSemilattice_706
v3
du_poset_790 ::
  T_BoundedMeetSemilattice_706 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Poset_282
du_poset_790 :: T_BoundedMeetSemilattice_706 -> T_Poset_282
du_poset_790 T_BoundedMeetSemilattice_706
v0
  = (T_MeetSemilattice_540 -> T_Poset_282) -> AgdaAny -> T_Poset_282
forall a b. a -> b
coe T_MeetSemilattice_540 -> T_Poset_282
du_poset_610 ((T_BoundedMeetSemilattice_706 -> T_MeetSemilattice_540)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_706 -> T_MeetSemilattice_540
du_meetSemilattice_784 (T_BoundedMeetSemilattice_706 -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_706
v0))
-- Relation.Binary.Lattice.BoundedMeetSemilattice._.preorder
d_preorder_792 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedMeetSemilattice_706 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Preorder_132
d_preorder_792 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedMeetSemilattice_706
-> T_Preorder_132
d_preorder_792 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedMeetSemilattice_706
v3 = T_BoundedMeetSemilattice_706 -> T_Preorder_132
du_preorder_792 T_BoundedMeetSemilattice_706
v3
du_preorder_792 ::
  T_BoundedMeetSemilattice_706 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Preorder_132
du_preorder_792 :: T_BoundedMeetSemilattice_706 -> T_Preorder_132
du_preorder_792 T_BoundedMeetSemilattice_706
v0
  = let v1 :: t
v1 = (T_BoundedMeetSemilattice_706 -> T_MeetSemilattice_540)
-> AgdaAny -> t
forall a b. a -> b
coe T_BoundedMeetSemilattice_706 -> T_MeetSemilattice_540
du_meetSemilattice_784 (T_BoundedMeetSemilattice_706 -> AgdaAny
forall a b. a -> b
coe T_BoundedMeetSemilattice_706
v0) in
    AgdaAny -> T_Preorder_132
forall a b. a -> b
coe
      ((T_Poset_282 -> T_Preorder_132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Poset_282 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_326
         ((T_MeetSemilattice_540 -> T_Poset_282) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_MeetSemilattice_540 -> T_Poset_282
du_poset_610 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Relation.Binary.Lattice.IsLattice
d_IsLattice_810 :: p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsLattice_810 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 = ()
data T_IsLattice_810
  = C_IsLattice'46'constructor_25911 MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_162
                                     (AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14)
                                     (AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14)
-- Relation.Binary.Lattice.IsLattice.isPartialOrder
d_isPartialOrder_834 ::
  T_IsLattice_810 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_162
d_isPartialOrder_834 :: T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 T_IsLattice_810
v0
  = case T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v0 of
      C_IsLattice'46'constructor_25911 T_IsPartialOrder_162
v1 AgdaAny -> AgdaAny -> T_Σ_14
v2 AgdaAny -> AgdaAny -> T_Σ_14
v3 -> T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
v1
      T_IsLattice_810
_ -> T_IsPartialOrder_162
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.IsLattice.supremum
d_supremum_836 ::
  T_IsLattice_810 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_supremum_836 :: T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_836 T_IsLattice_810
v0
  = case T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v0 of
      C_IsLattice'46'constructor_25911 T_IsPartialOrder_162
v1 AgdaAny -> AgdaAny -> T_Σ_14
v2 AgdaAny -> AgdaAny -> T_Σ_14
v3 -> (AgdaAny -> AgdaAny -> T_Σ_14) -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe AgdaAny -> AgdaAny -> T_Σ_14
v2
      T_IsLattice_810
_ -> AgdaAny -> AgdaAny -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.IsLattice.infimum
d_infimum_838 ::
  T_IsLattice_810 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_infimum_838 :: T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_838 T_IsLattice_810
v0
  = case T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v0 of
      C_IsLattice'46'constructor_25911 T_IsPartialOrder_162
v1 AgdaAny -> AgdaAny -> T_Σ_14
v2 AgdaAny -> AgdaAny -> T_Σ_14
v3 -> (AgdaAny -> AgdaAny -> T_Σ_14) -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe AgdaAny -> AgdaAny -> T_Σ_14
v3
      T_IsLattice_810
_ -> AgdaAny -> AgdaAny -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.IsLattice.isJoinSemilattice
d_isJoinSemilattice_840 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsLattice_810 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_840 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_810
-> T_IsJoinSemilattice_68
d_isJoinSemilattice_840 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsLattice_810
v8
  = T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 T_IsLattice_810
v8
du_isJoinSemilattice_840 ::
  T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 :: T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 T_IsLattice_810
v0
  = (T_IsPartialOrder_162
 -> (AgdaAny -> AgdaAny -> T_Σ_14) -> T_IsJoinSemilattice_68)
-> AgdaAny -> AgdaAny -> T_IsJoinSemilattice_68
forall a b. a -> b
coe
      T_IsPartialOrder_162
-> (AgdaAny -> AgdaAny -> T_Σ_14) -> T_IsJoinSemilattice_68
C_IsJoinSemilattice'46'constructor_2281
      ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v0)) ((T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_836 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v0))
-- Relation.Binary.Lattice.IsLattice.isMeetSemilattice
d_isMeetSemilattice_842 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsLattice_810 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_842 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_810
-> T_IsMeetSemilattice_438
d_isMeetSemilattice_842 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsLattice_810
v8
  = T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 T_IsLattice_810
v8
du_isMeetSemilattice_842 ::
  T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 :: T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 T_IsLattice_810
v0
  = (T_IsPartialOrder_162
 -> (AgdaAny -> AgdaAny -> T_Σ_14) -> T_IsMeetSemilattice_438)
-> AgdaAny -> AgdaAny -> T_IsMeetSemilattice_438
forall a b. a -> b
coe
      T_IsPartialOrder_162
-> (AgdaAny -> AgdaAny -> T_Σ_14) -> T_IsMeetSemilattice_438
C_IsMeetSemilattice'46'constructor_13939
      ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v0)) ((T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_838 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v0))
-- Relation.Binary.Lattice.IsLattice._.x≤x∨y
d_x'8804'x'8744'y_846 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsLattice_810 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8804'x'8744'y_846 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_810
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8804'x'8744'y_846 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsLattice_810
v8
  = T_IsLattice_810 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_846 T_IsLattice_810
v8
du_x'8804'x'8744'y_846 ::
  T_IsLattice_810 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_846 :: T_IsLattice_810 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_846 T_IsLattice_810
v0
  = (T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_96 ((T_IsLattice_810 -> T_IsJoinSemilattice_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v0))
-- Relation.Binary.Lattice.IsLattice._.y≤x∨y
d_y'8804'x'8744'y_848 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsLattice_810 -> AgdaAny -> AgdaAny -> AgdaAny
d_y'8804'x'8744'y_848 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_810
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_y'8804'x'8744'y_848 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsLattice_810
v8
  = T_IsLattice_810 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_848 T_IsLattice_810
v8
du_y'8804'x'8744'y_848 ::
  T_IsLattice_810 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_848 :: T_IsLattice_810 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_848 T_IsLattice_810
v0
  = (T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_108 ((T_IsLattice_810 -> T_IsJoinSemilattice_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v0))
-- Relation.Binary.Lattice.IsLattice._.∨-least
d_'8744''45'least_850 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsLattice_810 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'least_850 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_810
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'least_850 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsLattice_810
v8
  = T_IsLattice_810
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_850 T_IsLattice_810
v8
du_'8744''45'least_850 ::
  T_IsLattice_810 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_850 :: T_IsLattice_810
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_850 T_IsLattice_810
v0
  = (T_IsJoinSemilattice_68
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsJoinSemilattice_68
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_122 ((T_IsLattice_810 -> T_IsJoinSemilattice_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v0))
-- Relation.Binary.Lattice.IsLattice._.x∧y≤x
d_x'8743'y'8804'x_854 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsLattice_810 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'x_854 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_810
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'x_854 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsLattice_810
v8
  = T_IsLattice_810 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_854 T_IsLattice_810
v8
du_x'8743'y'8804'x_854 ::
  T_IsLattice_810 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_854 :: T_IsLattice_810 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_854 T_IsLattice_810
v0
  = (T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_466 ((T_IsLattice_810 -> T_IsMeetSemilattice_438) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v0))
-- Relation.Binary.Lattice.IsLattice._.x∧y≤y
d_x'8743'y'8804'y_856 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsLattice_810 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'y_856 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_810
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'y_856 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsLattice_810
v8
  = T_IsLattice_810 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_856 T_IsLattice_810
v8
du_x'8743'y'8804'y_856 ::
  T_IsLattice_810 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_856 :: T_IsLattice_810 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_856 T_IsLattice_810
v0
  = (T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_478 ((T_IsLattice_810 -> T_IsMeetSemilattice_438) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v0))
-- Relation.Binary.Lattice.IsLattice._.∧-greatest
d_'8743''45'greatest_858 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsLattice_810 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'greatest_858 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_810
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'greatest_858 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsLattice_810
v8
  = T_IsLattice_810
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_858 T_IsLattice_810
v8
du_'8743''45'greatest_858 ::
  T_IsLattice_810 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_858 :: T_IsLattice_810
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_858 T_IsLattice_810
v0
  = (T_IsMeetSemilattice_438
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMeetSemilattice_438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_492 ((T_IsLattice_810 -> T_IsMeetSemilattice_438) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v0))
-- Relation.Binary.Lattice.IsLattice._.antisym
d_antisym_862 ::
  T_IsLattice_810 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_862 :: T_IsLattice_810
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_862 T_IsLattice_810
v0
  = (T_IsPartialOrder_162
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_162
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_172
      ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v0))
-- Relation.Binary.Lattice.IsLattice._.isEquivalence
d_isEquivalence_864 ::
  T_IsLattice_810 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_864 :: T_IsLattice_810 -> T_IsEquivalence_26
d_isEquivalence_864 T_IsLattice_810
v0
  = (T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v0)))
-- Relation.Binary.Lattice.IsLattice._.isPreorder
d_isPreorder_866 ::
  T_IsLattice_810 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_866 :: T_IsLattice_810 -> T_IsPreorder_70
d_isPreorder_866 T_IsLattice_810
v0
  = (T_IsPartialOrder_162 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
      ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v0))
-- Relation.Binary.Lattice.IsLattice._.refl
d_refl_868 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsLattice_810 -> AgdaAny -> AgdaAny
d_refl_868 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_810
-> AgdaAny
-> AgdaAny
d_refl_868 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsLattice_810
v8 = T_IsLattice_810 -> AgdaAny -> AgdaAny
du_refl_868 T_IsLattice_810
v8
du_refl_868 :: T_IsLattice_810 -> AgdaAny -> AgdaAny
du_refl_868 :: T_IsLattice_810 -> AgdaAny -> AgdaAny
du_refl_868 T_IsLattice_810
v0
  = let v1 :: T_IsPartialOrder_162
v1 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsPreorder_70 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_98
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170 (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v1)))
-- Relation.Binary.Lattice.IsLattice._.reflexive
d_reflexive_870 ::
  T_IsLattice_810 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_870 :: T_IsLattice_810 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_870 T_IsLattice_810
v0
  = (T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v0)))
-- Relation.Binary.Lattice.IsLattice._.trans
d_trans_872 ::
  T_IsLattice_810 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_872 :: T_IsLattice_810
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_872 T_IsLattice_810
v0
  = (T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v0)))
-- Relation.Binary.Lattice.IsLattice._.∼-resp-≈
d_'8764''45'resp'45''8776'_874 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsLattice_810 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_874 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_810
-> T_Σ_14
d_'8764''45'resp'45''8776'_874 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsLattice_810
v8
  = T_IsLattice_810 -> T_Σ_14
du_'8764''45'resp'45''8776'_874 T_IsLattice_810
v8
du_'8764''45'resp'45''8776'_874 ::
  T_IsLattice_810 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_874 :: T_IsLattice_810 -> T_Σ_14
du_'8764''45'resp'45''8776'_874 T_IsLattice_810
v0
  = let v1 :: T_IsPartialOrder_162
v1 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      ((T_IsPreorder_70 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_112
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170 (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v1)))
-- Relation.Binary.Lattice.IsLattice._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_876 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsLattice_810 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_876 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_810
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_876 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7
                                    T_IsLattice_810
v8
  = T_IsLattice_810
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_876 T_IsLattice_810
v8
du_'8764''45'resp'691''45''8776'_876 ::
  T_IsLattice_810 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_876 :: T_IsLattice_810
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_876 T_IsLattice_810
v0
  = let v1 :: T_IsPartialOrder_162
v1 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_106
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170 (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v1)))
-- Relation.Binary.Lattice.IsLattice._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_878 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsLattice_810 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_878 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_810
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_878 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7
                                    T_IsLattice_810
v8
  = T_IsLattice_810
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_878 T_IsLattice_810
v8
du_'8764''45'resp'737''45''8776'_878 ::
  T_IsLattice_810 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_878 :: T_IsLattice_810
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_878 T_IsLattice_810
v0
  = let v1 :: T_IsPartialOrder_162
v1 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_100
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170 (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v1)))
-- Relation.Binary.Lattice.IsLattice._.Eq.isPartialEquivalence
d_isPartialEquivalence_882 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsLattice_810 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_882 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_810
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_882 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsLattice_810
v8
  = T_IsLattice_810 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_882 T_IsLattice_810
v8
du_isPartialEquivalence_882 ::
  T_IsLattice_810 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_882 :: T_IsLattice_810 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_882 T_IsLattice_810
v0
  = let v1 :: T_IsPartialOrder_162
v1 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPreorder_70
v2
             = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                 (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
               (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v2))))
-- Relation.Binary.Lattice.IsLattice._.Eq.refl
d_refl_884 :: T_IsLattice_810 -> AgdaAny -> AgdaAny
d_refl_884 :: T_IsLattice_810 -> AgdaAny -> AgdaAny
d_refl_884 T_IsLattice_810
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v0))))
-- Relation.Binary.Lattice.IsLattice._.Eq.reflexive
d_reflexive_886 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsLattice_810 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_886 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_810
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_886 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsLattice_810
v8
  = T_IsLattice_810 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_886 T_IsLattice_810
v8
du_reflexive_886 ::
  T_IsLattice_810 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_886 :: T_IsLattice_810 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_886 T_IsLattice_810
v0
  = let v1 :: T_IsPartialOrder_162
v1 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPreorder_70
v2
             = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                 (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                 (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v2))
              AgdaAny
v3))
-- Relation.Binary.Lattice.IsLattice._.Eq.sym
d_sym_888 ::
  T_IsLattice_810 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_888 :: T_IsLattice_810 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_888 T_IsLattice_810
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v0))))
-- Relation.Binary.Lattice.IsLattice._.Eq.trans
d_trans_890 ::
  T_IsLattice_810 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_890 :: T_IsLattice_810
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_890 T_IsLattice_810
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v0))))
-- Relation.Binary.Lattice.Lattice
d_Lattice_898 :: p -> p -> p -> T_Level_18
d_Lattice_898 p
a0 p
a1 p
a2 = ()
data T_Lattice_898
  = C_Lattice'46'constructor_30305 (AgdaAny -> AgdaAny -> AgdaAny)
                                   (AgdaAny -> AgdaAny -> AgdaAny) T_IsLattice_810
-- Relation.Binary.Lattice.Lattice.Carrier
d_Carrier_918 :: T_Lattice_898 -> ()
d_Carrier_918 :: T_Lattice_898 -> T_Level_18
d_Carrier_918 = T_Lattice_898 -> T_Level_18
forall a. a
erased
-- Relation.Binary.Lattice.Lattice._≈_
d__'8776'__920 :: T_Lattice_898 -> AgdaAny -> AgdaAny -> ()
d__'8776'__920 :: T_Lattice_898 -> AgdaAny -> AgdaAny -> T_Level_18
d__'8776'__920 = T_Lattice_898 -> AgdaAny -> AgdaAny -> T_Level_18
forall a. a
erased
-- Relation.Binary.Lattice.Lattice._≤_
d__'8804'__922 :: T_Lattice_898 -> AgdaAny -> AgdaAny -> ()
d__'8804'__922 :: T_Lattice_898 -> AgdaAny -> AgdaAny -> T_Level_18
d__'8804'__922 = T_Lattice_898 -> AgdaAny -> AgdaAny -> T_Level_18
forall a. a
erased
-- Relation.Binary.Lattice.Lattice._∨_
d__'8744'__924 :: T_Lattice_898 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__924 :: T_Lattice_898 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__924 T_Lattice_898
v0
  = case T_Lattice_898 -> T_Lattice_898
forall a b. a -> b
coe T_Lattice_898
v0 of
      C_Lattice'46'constructor_30305 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsLattice_810
v6 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_Lattice_898
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.Lattice._∧_
d__'8743'__926 :: T_Lattice_898 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__926 :: T_Lattice_898 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__926 T_Lattice_898
v0
  = case T_Lattice_898 -> T_Lattice_898
forall a b. a -> b
coe T_Lattice_898
v0 of
      C_Lattice'46'constructor_30305 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsLattice_810
v6 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v5
      T_Lattice_898
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.Lattice.isLattice
d_isLattice_928 :: T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 :: T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 T_Lattice_898
v0
  = case T_Lattice_898 -> T_Lattice_898
forall a b. a -> b
coe T_Lattice_898
v0 of
      C_Lattice'46'constructor_30305 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsLattice_810
v6 -> T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v6
      T_Lattice_898
_ -> T_IsLattice_810
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.Lattice._.antisym
d_antisym_932 ::
  T_Lattice_898 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_932 :: T_Lattice_898
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_932 T_Lattice_898
v0
  = (T_IsPartialOrder_162
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_162
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_172
      ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 ((T_Lattice_898 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (T_Lattice_898 -> AgdaAny
forall a b. a -> b
coe T_Lattice_898
v0)))
-- Relation.Binary.Lattice.Lattice._.infimum
d_infimum_934 ::
  T_Lattice_898 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_infimum_934 :: T_Lattice_898 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_934 T_Lattice_898
v0 = (T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_838 ((T_Lattice_898 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (T_Lattice_898 -> AgdaAny
forall a b. a -> b
coe T_Lattice_898
v0))
-- Relation.Binary.Lattice.Lattice._.isEquivalence
d_isEquivalence_936 ::
  T_Lattice_898 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_936 :: T_Lattice_898 -> T_IsEquivalence_26
d_isEquivalence_936 T_Lattice_898
v0
  = (T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 ((T_Lattice_898 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (T_Lattice_898 -> AgdaAny
forall a b. a -> b
coe T_Lattice_898
v0))))
-- Relation.Binary.Lattice.Lattice._.isJoinSemilattice
d_isJoinSemilattice_938 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_898 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_938 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Lattice_898
-> T_IsJoinSemilattice_68
d_isJoinSemilattice_938 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_Lattice_898
v3
  = T_Lattice_898 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_938 T_Lattice_898
v3
du_isJoinSemilattice_938 :: T_Lattice_898 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_938 :: T_Lattice_898 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_938 T_Lattice_898
v0
  = (T_IsLattice_810 -> T_IsJoinSemilattice_68)
-> AgdaAny -> T_IsJoinSemilattice_68
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 ((T_Lattice_898 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (T_Lattice_898 -> AgdaAny
forall a b. a -> b
coe T_Lattice_898
v0))
-- Relation.Binary.Lattice.Lattice._.isMeetSemilattice
d_isMeetSemilattice_940 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_898 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_940 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Lattice_898
-> T_IsMeetSemilattice_438
d_isMeetSemilattice_940 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_Lattice_898
v3
  = T_Lattice_898 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_940 T_Lattice_898
v3
du_isMeetSemilattice_940 ::
  T_Lattice_898 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_940 :: T_Lattice_898 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_940 T_Lattice_898
v0
  = (T_IsLattice_810 -> T_IsMeetSemilattice_438)
-> AgdaAny -> T_IsMeetSemilattice_438
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 ((T_Lattice_898 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (T_Lattice_898 -> AgdaAny
forall a b. a -> b
coe T_Lattice_898
v0))
-- Relation.Binary.Lattice.Lattice._.isPartialOrder
d_isPartialOrder_942 ::
  T_Lattice_898 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_162
d_isPartialOrder_942 :: T_Lattice_898 -> T_IsPartialOrder_162
d_isPartialOrder_942 T_Lattice_898
v0
  = (T_IsLattice_810 -> T_IsPartialOrder_162)
-> AgdaAny -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 ((T_Lattice_898 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (T_Lattice_898 -> AgdaAny
forall a b. a -> b
coe T_Lattice_898
v0))
-- Relation.Binary.Lattice.Lattice._.isPreorder
d_isPreorder_944 ::
  T_Lattice_898 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_944 :: T_Lattice_898 -> T_IsPreorder_70
d_isPreorder_944 T_Lattice_898
v0
  = (T_IsPartialOrder_162 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
      ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 ((T_Lattice_898 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (T_Lattice_898 -> AgdaAny
forall a b. a -> b
coe T_Lattice_898
v0)))
-- Relation.Binary.Lattice.Lattice._.refl
d_refl_946 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_898 -> AgdaAny -> AgdaAny
d_refl_946 :: T_Level_18
-> T_Level_18 -> T_Level_18 -> T_Lattice_898 -> AgdaAny -> AgdaAny
d_refl_946 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_Lattice_898
v3 = T_Lattice_898 -> AgdaAny -> AgdaAny
du_refl_946 T_Lattice_898
v3
du_refl_946 :: T_Lattice_898 -> AgdaAny -> AgdaAny
du_refl_946 :: T_Lattice_898 -> AgdaAny -> AgdaAny
du_refl_946 T_Lattice_898
v0
  = let v1 :: T_IsLattice_810
v1 = T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (T_Lattice_898 -> T_Lattice_898
forall a b. a -> b
coe T_Lattice_898
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_70 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_98
            ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
               (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v2))))
-- Relation.Binary.Lattice.Lattice._.reflexive
d_reflexive_948 ::
  T_Lattice_898 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_948 :: T_Lattice_898 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_948 T_Lattice_898
v0
  = (T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 ((T_Lattice_898 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (T_Lattice_898 -> AgdaAny
forall a b. a -> b
coe T_Lattice_898
v0))))
-- Relation.Binary.Lattice.Lattice._.supremum
d_supremum_950 ::
  T_Lattice_898 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_supremum_950 :: T_Lattice_898 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_950 T_Lattice_898
v0
  = (T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_836 ((T_Lattice_898 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (T_Lattice_898 -> AgdaAny
forall a b. a -> b
coe T_Lattice_898
v0))
-- Relation.Binary.Lattice.Lattice._.trans
d_trans_952 ::
  T_Lattice_898 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_952 :: T_Lattice_898
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_952 T_Lattice_898
v0
  = (T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 ((T_Lattice_898 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (T_Lattice_898 -> AgdaAny
forall a b. a -> b
coe T_Lattice_898
v0))))
-- Relation.Binary.Lattice.Lattice._.x∧y≤x
d_x'8743'y'8804'x_954 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_898 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'x_954 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Lattice_898
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'x_954 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_Lattice_898
v3 = T_Lattice_898 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_954 T_Lattice_898
v3
du_x'8743'y'8804'x_954 ::
  T_Lattice_898 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_954 :: T_Lattice_898 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_954 T_Lattice_898
v0
  = let v1 :: T_IsLattice_810
v1 = T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (T_Lattice_898 -> T_Lattice_898
forall a b. a -> b
coe T_Lattice_898
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_466 ((T_IsLattice_810 -> T_IsMeetSemilattice_438) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v1)))
-- Relation.Binary.Lattice.Lattice._.x∧y≤y
d_x'8743'y'8804'y_956 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_898 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'y_956 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Lattice_898
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'y_956 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_Lattice_898
v3 = T_Lattice_898 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_956 T_Lattice_898
v3
du_x'8743'y'8804'y_956 ::
  T_Lattice_898 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_956 :: T_Lattice_898 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_956 T_Lattice_898
v0
  = let v1 :: T_IsLattice_810
v1 = T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (T_Lattice_898 -> T_Lattice_898
forall a b. a -> b
coe T_Lattice_898
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_478 ((T_IsLattice_810 -> T_IsMeetSemilattice_438) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v1)))
-- Relation.Binary.Lattice.Lattice._.x≤x∨y
d_x'8804'x'8744'y_958 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_898 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8804'x'8744'y_958 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Lattice_898
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8804'x'8744'y_958 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_Lattice_898
v3 = T_Lattice_898 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_958 T_Lattice_898
v3
du_x'8804'x'8744'y_958 ::
  T_Lattice_898 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_958 :: T_Lattice_898 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_958 T_Lattice_898
v0
  = let v1 :: T_IsLattice_810
v1 = T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (T_Lattice_898 -> T_Lattice_898
forall a b. a -> b
coe T_Lattice_898
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_96 ((T_IsLattice_810 -> T_IsJoinSemilattice_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v1)))
-- Relation.Binary.Lattice.Lattice._.y≤x∨y
d_y'8804'x'8744'y_960 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_898 -> AgdaAny -> AgdaAny -> AgdaAny
d_y'8804'x'8744'y_960 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Lattice_898
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_y'8804'x'8744'y_960 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_Lattice_898
v3 = T_Lattice_898 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_960 T_Lattice_898
v3
du_y'8804'x'8744'y_960 ::
  T_Lattice_898 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_960 :: T_Lattice_898 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_960 T_Lattice_898
v0
  = let v1 :: T_IsLattice_810
v1 = T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (T_Lattice_898 -> T_Lattice_898
forall a b. a -> b
coe T_Lattice_898
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_108 ((T_IsLattice_810 -> T_IsJoinSemilattice_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v1)))
-- Relation.Binary.Lattice.Lattice._.∧-greatest
d_'8743''45'greatest_962 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_898 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'greatest_962 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Lattice_898
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'greatest_962 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_Lattice_898
v3
  = T_Lattice_898
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_962 T_Lattice_898
v3
du_'8743''45'greatest_962 ::
  T_Lattice_898 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_962 :: T_Lattice_898
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_962 T_Lattice_898
v0
  = let v1 :: T_IsLattice_810
v1 = T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (T_Lattice_898 -> T_Lattice_898
forall a b. a -> b
coe T_Lattice_898
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMeetSemilattice_438
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMeetSemilattice_438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_492 ((T_IsLattice_810 -> T_IsMeetSemilattice_438) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v1)))
-- Relation.Binary.Lattice.Lattice._.∨-least
d_'8744''45'least_964 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_898 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'least_964 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Lattice_898
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'least_964 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_Lattice_898
v3 = T_Lattice_898
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_964 T_Lattice_898
v3
du_'8744''45'least_964 ::
  T_Lattice_898 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_964 :: T_Lattice_898
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_964 T_Lattice_898
v0
  = let v1 :: T_IsLattice_810
v1 = T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (T_Lattice_898 -> T_Lattice_898
forall a b. a -> b
coe T_Lattice_898
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsJoinSemilattice_68
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsJoinSemilattice_68
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_122 ((T_IsLattice_810 -> T_IsJoinSemilattice_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v1)))
-- Relation.Binary.Lattice.Lattice._.∼-resp-≈
d_'8764''45'resp'45''8776'_966 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_898 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_966 :: T_Level_18 -> T_Level_18 -> T_Level_18 -> T_Lattice_898 -> T_Σ_14
d_'8764''45'resp'45''8776'_966 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_Lattice_898
v3
  = T_Lattice_898 -> T_Σ_14
du_'8764''45'resp'45''8776'_966 T_Lattice_898
v3
du_'8764''45'resp'45''8776'_966 ::
  T_Lattice_898 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_966 :: T_Lattice_898 -> T_Σ_14
du_'8764''45'resp'45''8776'_966 T_Lattice_898
v0
  = let v1 :: T_IsLattice_810
v1 = T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (T_Lattice_898 -> T_Lattice_898
forall a b. a -> b
coe T_Lattice_898
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_70 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_112
            ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
               (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v2))))
-- Relation.Binary.Lattice.Lattice._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_968 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_898 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_968 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Lattice_898
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_968 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_Lattice_898
v3
  = T_Lattice_898
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_968 T_Lattice_898
v3
du_'8764''45'resp'691''45''8776'_968 ::
  T_Lattice_898 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_968 :: T_Lattice_898
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_968 T_Lattice_898
v0
  = let v1 :: T_IsLattice_810
v1 = T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (T_Lattice_898 -> T_Lattice_898
forall a b. a -> b
coe T_Lattice_898
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_106
            ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
               (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v2))))
-- Relation.Binary.Lattice.Lattice._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_970 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_898 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_970 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Lattice_898
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_970 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_Lattice_898
v3
  = T_Lattice_898
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_970 T_Lattice_898
v3
du_'8764''45'resp'737''45''8776'_970 ::
  T_Lattice_898 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_970 :: T_Lattice_898
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_970 T_Lattice_898
v0
  = let v1 :: T_IsLattice_810
v1 = T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (T_Lattice_898 -> T_Lattice_898
forall a b. a -> b
coe T_Lattice_898
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_100
            ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
               (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v2))))
-- Relation.Binary.Lattice.Lattice._.Eq.isPartialEquivalence
d_isPartialEquivalence_974 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_898 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_974 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Lattice_898
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_974 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_Lattice_898
v3
  = T_Lattice_898 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_974 T_Lattice_898
v3
du_isPartialEquivalence_974 ::
  T_Lattice_898 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_974 :: T_Lattice_898 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_974 T_Lattice_898
v0
  = let v1 :: T_IsLattice_810
v1 = T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (T_Lattice_898 -> T_Lattice_898
forall a b. a -> b
coe T_Lattice_898
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreorder_70
v3
                = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                    (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                  (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v3)))))
-- Relation.Binary.Lattice.Lattice._.Eq.refl
d_refl_976 :: T_Lattice_898 -> AgdaAny -> AgdaAny
d_refl_976 :: T_Lattice_898 -> AgdaAny -> AgdaAny
d_refl_976 T_Lattice_898
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 ((T_Lattice_898 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (T_Lattice_898 -> AgdaAny
forall a b. a -> b
coe T_Lattice_898
v0)))))
-- Relation.Binary.Lattice.Lattice._.Eq.reflexive
d_reflexive_978 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_898 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_978 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Lattice_898
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_978 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_Lattice_898
v3 = T_Lattice_898 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_978 T_Lattice_898
v3
du_reflexive_978 ::
  T_Lattice_898 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_978 :: T_Lattice_898 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_978 T_Lattice_898
v0
  = let v1 :: T_IsLattice_810
v1 = T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (T_Lattice_898 -> T_Lattice_898
forall a b. a -> b
coe T_Lattice_898
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreorder_70
v3
                = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                    (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                    (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v3))
                 AgdaAny
v4)))
-- Relation.Binary.Lattice.Lattice._.Eq.sym
d_sym_980 ::
  T_Lattice_898 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_980 :: T_Lattice_898 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_980 T_Lattice_898
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 ((T_Lattice_898 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (T_Lattice_898 -> AgdaAny
forall a b. a -> b
coe T_Lattice_898
v0)))))
-- Relation.Binary.Lattice.Lattice._.Eq.trans
d_trans_982 ::
  T_Lattice_898 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_982 :: T_Lattice_898
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_982 T_Lattice_898
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 ((T_Lattice_898 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (T_Lattice_898 -> AgdaAny
forall a b. a -> b
coe T_Lattice_898
v0)))))
-- Relation.Binary.Lattice.Lattice.setoid
d_setoid_984 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_898 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_984 :: T_Level_18
-> T_Level_18 -> T_Level_18 -> T_Lattice_898 -> T_Setoid_44
d_setoid_984 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_Lattice_898
v3 = T_Lattice_898 -> T_Setoid_44
du_setoid_984 T_Lattice_898
v3
du_setoid_984 ::
  T_Lattice_898 -> MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_984 :: T_Lattice_898 -> T_Setoid_44
du_setoid_984 T_Lattice_898
v0
  = (T_IsEquivalence_26 -> T_Setoid_44)
-> T_IsEquivalence_26 -> T_Setoid_44
forall a b. a -> b
coe
      T_IsEquivalence_26 -> T_Setoid_44
MAlonzo.Code.Relation.Binary.Bundles.C_Setoid'46'constructor_727
      (T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 ((T_Lattice_898 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (T_Lattice_898 -> AgdaAny
forall a b. a -> b
coe T_Lattice_898
v0)))))
-- Relation.Binary.Lattice.Lattice.joinSemilattice
d_joinSemilattice_986 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_898 -> T_JoinSemilattice_170
d_joinSemilattice_986 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Lattice_898
-> T_JoinSemilattice_170
d_joinSemilattice_986 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_Lattice_898
v3 = T_Lattice_898 -> T_JoinSemilattice_170
du_joinSemilattice_986 T_Lattice_898
v3
du_joinSemilattice_986 :: T_Lattice_898 -> T_JoinSemilattice_170
du_joinSemilattice_986 :: T_Lattice_898 -> T_JoinSemilattice_170
du_joinSemilattice_986 T_Lattice_898
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsJoinSemilattice_68 -> T_JoinSemilattice_170)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_JoinSemilattice_170
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsJoinSemilattice_68 -> T_JoinSemilattice_170
C_JoinSemilattice'46'constructor_7027 (T_Lattice_898 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__924 (T_Lattice_898 -> T_Lattice_898
forall a b. a -> b
coe T_Lattice_898
v0))
      ((T_IsLattice_810 -> T_IsJoinSemilattice_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 ((T_Lattice_898 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (T_Lattice_898 -> AgdaAny
forall a b. a -> b
coe T_Lattice_898
v0)))
-- Relation.Binary.Lattice.Lattice.meetSemilattice
d_meetSemilattice_988 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_898 -> T_MeetSemilattice_540
d_meetSemilattice_988 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Lattice_898
-> T_MeetSemilattice_540
d_meetSemilattice_988 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_Lattice_898
v3 = T_Lattice_898 -> T_MeetSemilattice_540
du_meetSemilattice_988 T_Lattice_898
v3
du_meetSemilattice_988 :: T_Lattice_898 -> T_MeetSemilattice_540
du_meetSemilattice_988 :: T_Lattice_898 -> T_MeetSemilattice_540
du_meetSemilattice_988 T_Lattice_898
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsMeetSemilattice_438 -> T_MeetSemilattice_540)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_MeetSemilattice_540
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMeetSemilattice_438 -> T_MeetSemilattice_540
C_MeetSemilattice'46'constructor_18685 (T_Lattice_898 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__926 (T_Lattice_898 -> T_Lattice_898
forall a b. a -> b
coe T_Lattice_898
v0))
      ((T_IsLattice_810 -> T_IsMeetSemilattice_438) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 ((T_Lattice_898 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (T_Lattice_898 -> AgdaAny
forall a b. a -> b
coe T_Lattice_898
v0)))
-- Relation.Binary.Lattice.Lattice._.poset
d_poset_992 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_898 -> MAlonzo.Code.Relation.Binary.Bundles.T_Poset_282
d_poset_992 :: T_Level_18
-> T_Level_18 -> T_Level_18 -> T_Lattice_898 -> T_Poset_282
d_poset_992 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_Lattice_898
v3 = T_Lattice_898 -> T_Poset_282
du_poset_992 T_Lattice_898
v3
du_poset_992 ::
  T_Lattice_898 -> MAlonzo.Code.Relation.Binary.Bundles.T_Poset_282
du_poset_992 :: T_Lattice_898 -> T_Poset_282
du_poset_992 T_Lattice_898
v0
  = (T_JoinSemilattice_170 -> T_Poset_282) -> AgdaAny -> T_Poset_282
forall a b. a -> b
coe T_JoinSemilattice_170 -> T_Poset_282
du_poset_240 ((T_Lattice_898 -> T_JoinSemilattice_170) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_898 -> T_JoinSemilattice_170
du_joinSemilattice_986 (T_Lattice_898 -> AgdaAny
forall a b. a -> b
coe T_Lattice_898
v0))
-- Relation.Binary.Lattice.Lattice._.preorder
d_preorder_994 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_Lattice_898 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Preorder_132
d_preorder_994 :: T_Level_18
-> T_Level_18 -> T_Level_18 -> T_Lattice_898 -> T_Preorder_132
d_preorder_994 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_Lattice_898
v3 = T_Lattice_898 -> T_Preorder_132
du_preorder_994 T_Lattice_898
v3
du_preorder_994 ::
  T_Lattice_898 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Preorder_132
du_preorder_994 :: T_Lattice_898 -> T_Preorder_132
du_preorder_994 T_Lattice_898
v0
  = let v1 :: t
v1 = (T_Lattice_898 -> T_JoinSemilattice_170) -> AgdaAny -> t
forall a b. a -> b
coe T_Lattice_898 -> T_JoinSemilattice_170
du_joinSemilattice_986 (T_Lattice_898 -> AgdaAny
forall a b. a -> b
coe T_Lattice_898
v0) in
    AgdaAny -> T_Preorder_132
forall a b. a -> b
coe
      ((T_Poset_282 -> T_Preorder_132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Poset_282 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_326
         ((T_JoinSemilattice_170 -> T_Poset_282) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_170 -> T_Poset_282
du_poset_240 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Relation.Binary.Lattice.IsDistributiveLattice
d_IsDistributiveLattice_1012 :: p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsDistributiveLattice_1012 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 = ()
data T_IsDistributiveLattice_1012
  = C_IsDistributiveLattice'46'constructor_33235 T_IsLattice_810
                                                 (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Relation.Binary.Lattice.IsDistributiveLattice.isLattice
d_isLattice_1034 :: T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 :: T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 T_IsDistributiveLattice_1012
v0
  = case T_IsDistributiveLattice_1012 -> T_IsDistributiveLattice_1012
forall a b. a -> b
coe T_IsDistributiveLattice_1012
v0 of
      C_IsDistributiveLattice'46'constructor_33235 T_IsLattice_810
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v1
      T_IsDistributiveLattice_1012
_ -> T_IsLattice_810
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.IsDistributiveLattice.∧-distribˡ-∨
d_'8743''45'distrib'737''45''8744'_1036 ::
  T_IsDistributiveLattice_1012 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'distrib'737''45''8744'_1036 :: T_IsDistributiveLattice_1012
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'distrib'737''45''8744'_1036 T_IsDistributiveLattice_1012
v0
  = case T_IsDistributiveLattice_1012 -> T_IsDistributiveLattice_1012
forall a b. a -> b
coe T_IsDistributiveLattice_1012
v0 of
      C_IsDistributiveLattice'46'constructor_33235 T_IsLattice_810
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2
      T_IsDistributiveLattice_1012
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.IsDistributiveLattice._.antisym
d_antisym_1040 ::
  T_IsDistributiveLattice_1012 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_1040 :: T_IsDistributiveLattice_1012
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_1040 T_IsDistributiveLattice_1012
v0
  = (T_IsPartialOrder_162
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_162
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_172
      ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 ((T_IsDistributiveLattice_1012 -> T_IsLattice_810)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 (T_IsDistributiveLattice_1012 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_1012
v0)))
-- Relation.Binary.Lattice.IsDistributiveLattice._.infimum
d_infimum_1042 ::
  T_IsDistributiveLattice_1012 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_infimum_1042 :: T_IsDistributiveLattice_1012 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_1042 T_IsDistributiveLattice_1012
v0
  = (T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_838 ((T_IsDistributiveLattice_1012 -> T_IsLattice_810)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 (T_IsDistributiveLattice_1012 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_1012
v0))
-- Relation.Binary.Lattice.IsDistributiveLattice._.isEquivalence
d_isEquivalence_1044 ::
  T_IsDistributiveLattice_1012 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1044 :: T_IsDistributiveLattice_1012 -> T_IsEquivalence_26
d_isEquivalence_1044 T_IsDistributiveLattice_1012
v0
  = (T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 ((T_IsDistributiveLattice_1012 -> T_IsLattice_810)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 (T_IsDistributiveLattice_1012 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_1012
v0))))
-- Relation.Binary.Lattice.IsDistributiveLattice._.isJoinSemilattice
d_isJoinSemilattice_1046 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_1012 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_1046 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_1012
-> T_IsJoinSemilattice_68
d_isJoinSemilattice_1046 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsDistributiveLattice_1012
v8
  = T_IsDistributiveLattice_1012 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_1046 T_IsDistributiveLattice_1012
v8
du_isJoinSemilattice_1046 ::
  T_IsDistributiveLattice_1012 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_1046 :: T_IsDistributiveLattice_1012 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_1046 T_IsDistributiveLattice_1012
v0
  = (T_IsLattice_810 -> T_IsJoinSemilattice_68)
-> AgdaAny -> T_IsJoinSemilattice_68
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 ((T_IsDistributiveLattice_1012 -> T_IsLattice_810)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 (T_IsDistributiveLattice_1012 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_1012
v0))
-- Relation.Binary.Lattice.IsDistributiveLattice._.isMeetSemilattice
d_isMeetSemilattice_1048 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_1012 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_1048 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_1012
-> T_IsMeetSemilattice_438
d_isMeetSemilattice_1048 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsDistributiveLattice_1012
v8
  = T_IsDistributiveLattice_1012 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_1048 T_IsDistributiveLattice_1012
v8
du_isMeetSemilattice_1048 ::
  T_IsDistributiveLattice_1012 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_1048 :: T_IsDistributiveLattice_1012 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_1048 T_IsDistributiveLattice_1012
v0
  = (T_IsLattice_810 -> T_IsMeetSemilattice_438)
-> AgdaAny -> T_IsMeetSemilattice_438
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 ((T_IsDistributiveLattice_1012 -> T_IsLattice_810)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 (T_IsDistributiveLattice_1012 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_1012
v0))
-- Relation.Binary.Lattice.IsDistributiveLattice._.isPartialOrder
d_isPartialOrder_1050 ::
  T_IsDistributiveLattice_1012 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_162
d_isPartialOrder_1050 :: T_IsDistributiveLattice_1012 -> T_IsPartialOrder_162
d_isPartialOrder_1050 T_IsDistributiveLattice_1012
v0
  = (T_IsLattice_810 -> T_IsPartialOrder_162)
-> AgdaAny -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 ((T_IsDistributiveLattice_1012 -> T_IsLattice_810)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 (T_IsDistributiveLattice_1012 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_1012
v0))
-- Relation.Binary.Lattice.IsDistributiveLattice._.isPreorder
d_isPreorder_1052 ::
  T_IsDistributiveLattice_1012 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_1052 :: T_IsDistributiveLattice_1012 -> T_IsPreorder_70
d_isPreorder_1052 T_IsDistributiveLattice_1012
v0
  = (T_IsPartialOrder_162 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
      ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 ((T_IsDistributiveLattice_1012 -> T_IsLattice_810)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 (T_IsDistributiveLattice_1012 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_1012
v0)))
-- Relation.Binary.Lattice.IsDistributiveLattice._.refl
d_refl_1054 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_1012 -> AgdaAny -> AgdaAny
d_refl_1054 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_1012
-> AgdaAny
-> AgdaAny
d_refl_1054 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsDistributiveLattice_1012
v8 = T_IsDistributiveLattice_1012 -> AgdaAny -> AgdaAny
du_refl_1054 T_IsDistributiveLattice_1012
v8
du_refl_1054 :: T_IsDistributiveLattice_1012 -> AgdaAny -> AgdaAny
du_refl_1054 :: T_IsDistributiveLattice_1012 -> AgdaAny -> AgdaAny
du_refl_1054 T_IsDistributiveLattice_1012
v0
  = let v1 :: T_IsLattice_810
v1 = T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 (T_IsDistributiveLattice_1012 -> T_IsDistributiveLattice_1012
forall a b. a -> b
coe T_IsDistributiveLattice_1012
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_70 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_98
            ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
               (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v2))))
-- Relation.Binary.Lattice.IsDistributiveLattice._.reflexive
d_reflexive_1056 ::
  T_IsDistributiveLattice_1012 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_1056 :: T_IsDistributiveLattice_1012
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_1056 T_IsDistributiveLattice_1012
v0
  = (T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 ((T_IsDistributiveLattice_1012 -> T_IsLattice_810)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 (T_IsDistributiveLattice_1012 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_1012
v0))))
-- Relation.Binary.Lattice.IsDistributiveLattice._.supremum
d_supremum_1058 ::
  T_IsDistributiveLattice_1012 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_supremum_1058 :: T_IsDistributiveLattice_1012 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_1058 T_IsDistributiveLattice_1012
v0
  = (T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_836 ((T_IsDistributiveLattice_1012 -> T_IsLattice_810)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 (T_IsDistributiveLattice_1012 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_1012
v0))
-- Relation.Binary.Lattice.IsDistributiveLattice._.trans
d_trans_1060 ::
  T_IsDistributiveLattice_1012 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1060 :: T_IsDistributiveLattice_1012
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1060 T_IsDistributiveLattice_1012
v0
  = (T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 ((T_IsDistributiveLattice_1012 -> T_IsLattice_810)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 (T_IsDistributiveLattice_1012 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_1012
v0))))
-- Relation.Binary.Lattice.IsDistributiveLattice._.x∧y≤x
d_x'8743'y'8804'x_1062 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_1012 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'x_1062 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_1012
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'x_1062 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsDistributiveLattice_1012
v8
  = T_IsDistributiveLattice_1012 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_1062 T_IsDistributiveLattice_1012
v8
du_x'8743'y'8804'x_1062 ::
  T_IsDistributiveLattice_1012 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_1062 :: T_IsDistributiveLattice_1012 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_1062 T_IsDistributiveLattice_1012
v0
  = let v1 :: T_IsLattice_810
v1 = T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 (T_IsDistributiveLattice_1012 -> T_IsDistributiveLattice_1012
forall a b. a -> b
coe T_IsDistributiveLattice_1012
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_466 ((T_IsLattice_810 -> T_IsMeetSemilattice_438) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v1)))
-- Relation.Binary.Lattice.IsDistributiveLattice._.x∧y≤y
d_x'8743'y'8804'y_1064 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_1012 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'y_1064 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_1012
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'y_1064 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsDistributiveLattice_1012
v8
  = T_IsDistributiveLattice_1012 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_1064 T_IsDistributiveLattice_1012
v8
du_x'8743'y'8804'y_1064 ::
  T_IsDistributiveLattice_1012 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_1064 :: T_IsDistributiveLattice_1012 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_1064 T_IsDistributiveLattice_1012
v0
  = let v1 :: T_IsLattice_810
v1 = T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 (T_IsDistributiveLattice_1012 -> T_IsDistributiveLattice_1012
forall a b. a -> b
coe T_IsDistributiveLattice_1012
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_478 ((T_IsLattice_810 -> T_IsMeetSemilattice_438) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v1)))
-- Relation.Binary.Lattice.IsDistributiveLattice._.x≤x∨y
d_x'8804'x'8744'y_1066 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_1012 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8804'x'8744'y_1066 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_1012
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8804'x'8744'y_1066 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsDistributiveLattice_1012
v8
  = T_IsDistributiveLattice_1012 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_1066 T_IsDistributiveLattice_1012
v8
du_x'8804'x'8744'y_1066 ::
  T_IsDistributiveLattice_1012 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_1066 :: T_IsDistributiveLattice_1012 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_1066 T_IsDistributiveLattice_1012
v0
  = let v1 :: T_IsLattice_810
v1 = T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 (T_IsDistributiveLattice_1012 -> T_IsDistributiveLattice_1012
forall a b. a -> b
coe T_IsDistributiveLattice_1012
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_96 ((T_IsLattice_810 -> T_IsJoinSemilattice_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v1)))
-- Relation.Binary.Lattice.IsDistributiveLattice._.y≤x∨y
d_y'8804'x'8744'y_1068 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_1012 -> AgdaAny -> AgdaAny -> AgdaAny
d_y'8804'x'8744'y_1068 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_1012
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_y'8804'x'8744'y_1068 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsDistributiveLattice_1012
v8
  = T_IsDistributiveLattice_1012 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_1068 T_IsDistributiveLattice_1012
v8
du_y'8804'x'8744'y_1068 ::
  T_IsDistributiveLattice_1012 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_1068 :: T_IsDistributiveLattice_1012 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_1068 T_IsDistributiveLattice_1012
v0
  = let v1 :: T_IsLattice_810
v1 = T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 (T_IsDistributiveLattice_1012 -> T_IsDistributiveLattice_1012
forall a b. a -> b
coe T_IsDistributiveLattice_1012
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_108 ((T_IsLattice_810 -> T_IsJoinSemilattice_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v1)))
-- Relation.Binary.Lattice.IsDistributiveLattice._.∧-greatest
d_'8743''45'greatest_1070 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_1012 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'greatest_1070 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_1012
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'greatest_1070 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsDistributiveLattice_1012
v8
  = T_IsDistributiveLattice_1012
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_1070 T_IsDistributiveLattice_1012
v8
du_'8743''45'greatest_1070 ::
  T_IsDistributiveLattice_1012 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_1070 :: T_IsDistributiveLattice_1012
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_1070 T_IsDistributiveLattice_1012
v0
  = let v1 :: T_IsLattice_810
v1 = T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 (T_IsDistributiveLattice_1012 -> T_IsDistributiveLattice_1012
forall a b. a -> b
coe T_IsDistributiveLattice_1012
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMeetSemilattice_438
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMeetSemilattice_438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_492 ((T_IsLattice_810 -> T_IsMeetSemilattice_438) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v1)))
-- Relation.Binary.Lattice.IsDistributiveLattice._.∨-least
d_'8744''45'least_1072 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_1012 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'least_1072 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_1012
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'least_1072 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsDistributiveLattice_1012
v8
  = T_IsDistributiveLattice_1012
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_1072 T_IsDistributiveLattice_1012
v8
du_'8744''45'least_1072 ::
  T_IsDistributiveLattice_1012 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_1072 :: T_IsDistributiveLattice_1012
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_1072 T_IsDistributiveLattice_1012
v0
  = let v1 :: T_IsLattice_810
v1 = T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 (T_IsDistributiveLattice_1012 -> T_IsDistributiveLattice_1012
forall a b. a -> b
coe T_IsDistributiveLattice_1012
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsJoinSemilattice_68
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsJoinSemilattice_68
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_122 ((T_IsLattice_810 -> T_IsJoinSemilattice_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v1)))
-- Relation.Binary.Lattice.IsDistributiveLattice._.∼-resp-≈
d_'8764''45'resp'45''8776'_1074 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_1012 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_1074 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_1012
-> T_Σ_14
d_'8764''45'resp'45''8776'_1074 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsDistributiveLattice_1012
v8
  = T_IsDistributiveLattice_1012 -> T_Σ_14
du_'8764''45'resp'45''8776'_1074 T_IsDistributiveLattice_1012
v8
du_'8764''45'resp'45''8776'_1074 ::
  T_IsDistributiveLattice_1012 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_1074 :: T_IsDistributiveLattice_1012 -> T_Σ_14
du_'8764''45'resp'45''8776'_1074 T_IsDistributiveLattice_1012
v0
  = let v1 :: T_IsLattice_810
v1 = T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 (T_IsDistributiveLattice_1012 -> T_IsDistributiveLattice_1012
forall a b. a -> b
coe T_IsDistributiveLattice_1012
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_70 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_112
            ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
               (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v2))))
-- Relation.Binary.Lattice.IsDistributiveLattice._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_1076 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_1012 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_1076 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_1012
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_1076 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6
                                     ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsDistributiveLattice_1012
v8
  = T_IsDistributiveLattice_1012
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_1076 T_IsDistributiveLattice_1012
v8
du_'8764''45'resp'691''45''8776'_1076 ::
  T_IsDistributiveLattice_1012 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_1076 :: T_IsDistributiveLattice_1012
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_1076 T_IsDistributiveLattice_1012
v0
  = let v1 :: T_IsLattice_810
v1 = T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 (T_IsDistributiveLattice_1012 -> T_IsDistributiveLattice_1012
forall a b. a -> b
coe T_IsDistributiveLattice_1012
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_106
            ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
               (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v2))))
-- Relation.Binary.Lattice.IsDistributiveLattice._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_1078 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_1012 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_1078 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_1012
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_1078 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6
                                     ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsDistributiveLattice_1012
v8
  = T_IsDistributiveLattice_1012
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_1078 T_IsDistributiveLattice_1012
v8
du_'8764''45'resp'737''45''8776'_1078 ::
  T_IsDistributiveLattice_1012 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_1078 :: T_IsDistributiveLattice_1012
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_1078 T_IsDistributiveLattice_1012
v0
  = let v1 :: T_IsLattice_810
v1 = T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 (T_IsDistributiveLattice_1012 -> T_IsDistributiveLattice_1012
forall a b. a -> b
coe T_IsDistributiveLattice_1012
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_100
            ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
               (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v2))))
-- Relation.Binary.Lattice.IsDistributiveLattice._.Eq.isPartialEquivalence
d_isPartialEquivalence_1082 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_1012 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1082 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_1012
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1082 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsDistributiveLattice_1012
v8
  = T_IsDistributiveLattice_1012 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1082 T_IsDistributiveLattice_1012
v8
du_isPartialEquivalence_1082 ::
  T_IsDistributiveLattice_1012 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1082 :: T_IsDistributiveLattice_1012 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1082 T_IsDistributiveLattice_1012
v0
  = let v1 :: T_IsLattice_810
v1 = T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 (T_IsDistributiveLattice_1012 -> T_IsDistributiveLattice_1012
forall a b. a -> b
coe T_IsDistributiveLattice_1012
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreorder_70
v3
                = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                    (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                  (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v3)))))
-- Relation.Binary.Lattice.IsDistributiveLattice._.Eq.refl
d_refl_1084 :: T_IsDistributiveLattice_1012 -> AgdaAny -> AgdaAny
d_refl_1084 :: T_IsDistributiveLattice_1012 -> AgdaAny -> AgdaAny
d_refl_1084 T_IsDistributiveLattice_1012
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 ((T_IsDistributiveLattice_1012 -> T_IsLattice_810)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 (T_IsDistributiveLattice_1012 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_1012
v0)))))
-- Relation.Binary.Lattice.IsDistributiveLattice._.Eq.reflexive
d_reflexive_1086 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_1012 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1086 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_1012
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1086 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsDistributiveLattice_1012
v8
  = T_IsDistributiveLattice_1012
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1086 T_IsDistributiveLattice_1012
v8
du_reflexive_1086 ::
  T_IsDistributiveLattice_1012 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1086 :: T_IsDistributiveLattice_1012
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1086 T_IsDistributiveLattice_1012
v0
  = let v1 :: T_IsLattice_810
v1 = T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 (T_IsDistributiveLattice_1012 -> T_IsDistributiveLattice_1012
forall a b. a -> b
coe T_IsDistributiveLattice_1012
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreorder_70
v3
                = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                    (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                    (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v3))
                 AgdaAny
v4)))
-- Relation.Binary.Lattice.IsDistributiveLattice._.Eq.sym
d_sym_1088 ::
  T_IsDistributiveLattice_1012 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1088 :: T_IsDistributiveLattice_1012
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1088 T_IsDistributiveLattice_1012
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 ((T_IsDistributiveLattice_1012 -> T_IsLattice_810)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 (T_IsDistributiveLattice_1012 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_1012
v0)))))
-- Relation.Binary.Lattice.IsDistributiveLattice._.Eq.trans
d_trans_1090 ::
  T_IsDistributiveLattice_1012 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1090 :: T_IsDistributiveLattice_1012
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1090 T_IsDistributiveLattice_1012
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 ((T_IsDistributiveLattice_1012 -> T_IsLattice_810)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 (T_IsDistributiveLattice_1012 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_1012
v0)))))
-- Relation.Binary.Lattice.DistributiveLattice
d_DistributiveLattice_1098 :: p -> p -> p -> T_Level_18
d_DistributiveLattice_1098 p
a0 p
a1 p
a2 = ()
data T_DistributiveLattice_1098
  = C_DistributiveLattice'46'constructor_36391 (AgdaAny ->
                                                AgdaAny -> AgdaAny)
                                               (AgdaAny -> AgdaAny -> AgdaAny)
                                               T_IsDistributiveLattice_1012
-- Relation.Binary.Lattice.DistributiveLattice.Carrier
d_Carrier_1118 :: T_DistributiveLattice_1098 -> ()
d_Carrier_1118 :: T_DistributiveLattice_1098 -> T_Level_18
d_Carrier_1118 = T_DistributiveLattice_1098 -> T_Level_18
forall a. a
erased
-- Relation.Binary.Lattice.DistributiveLattice._≈_
d__'8776'__1120 ::
  T_DistributiveLattice_1098 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1120 :: T_DistributiveLattice_1098 -> AgdaAny -> AgdaAny -> T_Level_18
d__'8776'__1120 = T_DistributiveLattice_1098 -> AgdaAny -> AgdaAny -> T_Level_18
forall a. a
erased
-- Relation.Binary.Lattice.DistributiveLattice._≤_
d__'8804'__1122 ::
  T_DistributiveLattice_1098 -> AgdaAny -> AgdaAny -> ()
d__'8804'__1122 :: T_DistributiveLattice_1098 -> AgdaAny -> AgdaAny -> T_Level_18
d__'8804'__1122 = T_DistributiveLattice_1098 -> AgdaAny -> AgdaAny -> T_Level_18
forall a. a
erased
-- Relation.Binary.Lattice.DistributiveLattice._∨_
d__'8744'__1124 ::
  T_DistributiveLattice_1098 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__1124 :: T_DistributiveLattice_1098 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__1124 T_DistributiveLattice_1098
v0
  = case T_DistributiveLattice_1098 -> T_DistributiveLattice_1098
forall a b. a -> b
coe T_DistributiveLattice_1098
v0 of
      C_DistributiveLattice'46'constructor_36391 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsDistributiveLattice_1012
v6 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_DistributiveLattice_1098
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.DistributiveLattice._∧_
d__'8743'__1126 ::
  T_DistributiveLattice_1098 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__1126 :: T_DistributiveLattice_1098 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__1126 T_DistributiveLattice_1098
v0
  = case T_DistributiveLattice_1098 -> T_DistributiveLattice_1098
forall a b. a -> b
coe T_DistributiveLattice_1098
v0 of
      C_DistributiveLattice'46'constructor_36391 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsDistributiveLattice_1012
v6 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v5
      T_DistributiveLattice_1098
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.DistributiveLattice.isDistributiveLattice
d_isDistributiveLattice_1128 ::
  T_DistributiveLattice_1098 -> T_IsDistributiveLattice_1012
d_isDistributiveLattice_1128 :: T_DistributiveLattice_1098 -> T_IsDistributiveLattice_1012
d_isDistributiveLattice_1128 T_DistributiveLattice_1098
v0
  = case T_DistributiveLattice_1098 -> T_DistributiveLattice_1098
forall a b. a -> b
coe T_DistributiveLattice_1098
v0 of
      C_DistributiveLattice'46'constructor_36391 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 T_IsDistributiveLattice_1012
v6 -> T_IsDistributiveLattice_1012 -> T_IsDistributiveLattice_1012
forall a b. a -> b
coe T_IsDistributiveLattice_1012
v6
      T_DistributiveLattice_1098
_ -> T_IsDistributiveLattice_1012
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.DistributiveLattice._.∧-distribˡ-∨
d_'8743''45'distrib'737''45''8744'_1132 ::
  T_DistributiveLattice_1098 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'distrib'737''45''8744'_1132 :: T_DistributiveLattice_1098
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'distrib'737''45''8744'_1132 T_DistributiveLattice_1098
v0
  = (T_IsDistributiveLattice_1012
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsDistributiveLattice_1012
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'distrib'737''45''8744'_1036
      ((T_DistributiveLattice_1098 -> T_IsDistributiveLattice_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098 -> T_IsDistributiveLattice_1012
d_isDistributiveLattice_1128 (T_DistributiveLattice_1098 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098
v0))
-- Relation.Binary.Lattice.DistributiveLattice._.isLattice
d_isLattice_1136 :: T_DistributiveLattice_1098 -> T_IsLattice_810
d_isLattice_1136 :: T_DistributiveLattice_1098 -> T_IsLattice_810
d_isLattice_1136 T_DistributiveLattice_1098
v0
  = (T_IsDistributiveLattice_1012 -> T_IsLattice_810)
-> AgdaAny -> T_IsLattice_810
forall a b. a -> b
coe T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 ((T_DistributiveLattice_1098 -> T_IsDistributiveLattice_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098 -> T_IsDistributiveLattice_1012
d_isDistributiveLattice_1128 (T_DistributiveLattice_1098 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098
v0))
-- Relation.Binary.Lattice.DistributiveLattice.lattice
d_lattice_1138 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1098 -> T_Lattice_898
d_lattice_1138 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_DistributiveLattice_1098
-> T_Lattice_898
d_lattice_1138 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_DistributiveLattice_1098
v3 = T_DistributiveLattice_1098 -> T_Lattice_898
du_lattice_1138 T_DistributiveLattice_1098
v3
du_lattice_1138 :: T_DistributiveLattice_1098 -> T_Lattice_898
du_lattice_1138 :: T_DistributiveLattice_1098 -> T_Lattice_898
du_lattice_1138 T_DistributiveLattice_1098
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsLattice_810
 -> T_Lattice_898)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_810
-> T_Lattice_898
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_810
-> T_Lattice_898
C_Lattice'46'constructor_30305 (T_DistributiveLattice_1098 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__1124 (T_DistributiveLattice_1098 -> T_DistributiveLattice_1098
forall a b. a -> b
coe T_DistributiveLattice_1098
v0))
      (T_DistributiveLattice_1098 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__1126 (T_DistributiveLattice_1098 -> T_DistributiveLattice_1098
forall a b. a -> b
coe T_DistributiveLattice_1098
v0))
      (T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 ((T_DistributiveLattice_1098 -> T_IsDistributiveLattice_1012)
-> AgdaAny -> T_IsDistributiveLattice_1012
forall a b. a -> b
coe T_DistributiveLattice_1098 -> T_IsDistributiveLattice_1012
d_isDistributiveLattice_1128 (T_DistributiveLattice_1098 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098
v0)))
-- Relation.Binary.Lattice.DistributiveLattice._.antisym
d_antisym_1142 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1098 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_1142 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_DistributiveLattice_1098
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_antisym_1142 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_DistributiveLattice_1098
v3 = T_DistributiveLattice_1098
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_antisym_1142 T_DistributiveLattice_1098
v3
du_antisym_1142 ::
  T_DistributiveLattice_1098 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_antisym_1142 :: T_DistributiveLattice_1098
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_antisym_1142 T_DistributiveLattice_1098
v0
  = (T_IsPartialOrder_162
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_162
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_172
      ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
         ((T_IsDistributiveLattice_1012 -> T_IsLattice_810)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 ((T_DistributiveLattice_1098 -> T_IsDistributiveLattice_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098 -> T_IsDistributiveLattice_1012
d_isDistributiveLattice_1128 (T_DistributiveLattice_1098 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098
v0))))
-- Relation.Binary.Lattice.DistributiveLattice._.infimum
d_infimum_1144 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1098 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_infimum_1144 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_DistributiveLattice_1098
-> AgdaAny
-> AgdaAny
-> T_Σ_14
d_infimum_1144 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_DistributiveLattice_1098
v3 = T_DistributiveLattice_1098 -> AgdaAny -> AgdaAny -> T_Σ_14
du_infimum_1144 T_DistributiveLattice_1098
v3
du_infimum_1144 ::
  T_DistributiveLattice_1098 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_infimum_1144 :: T_DistributiveLattice_1098 -> AgdaAny -> AgdaAny -> T_Σ_14
du_infimum_1144 T_DistributiveLattice_1098
v0
  = (T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_838
      ((T_IsDistributiveLattice_1012 -> T_IsLattice_810)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 ((T_DistributiveLattice_1098 -> T_IsDistributiveLattice_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098 -> T_IsDistributiveLattice_1012
d_isDistributiveLattice_1128 (T_DistributiveLattice_1098 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098
v0)))
-- Relation.Binary.Lattice.DistributiveLattice._.isEquivalence
d_isEquivalence_1146 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1098 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1146 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_DistributiveLattice_1098
-> T_IsEquivalence_26
d_isEquivalence_1146 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_DistributiveLattice_1098
v3 = T_DistributiveLattice_1098 -> T_IsEquivalence_26
du_isEquivalence_1146 T_DistributiveLattice_1098
v3
du_isEquivalence_1146 ::
  T_DistributiveLattice_1098 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_1146 :: T_DistributiveLattice_1098 -> T_IsEquivalence_26
du_isEquivalence_1146 T_DistributiveLattice_1098
v0
  = (T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
            ((T_IsDistributiveLattice_1012 -> T_IsLattice_810)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 ((T_DistributiveLattice_1098 -> T_IsDistributiveLattice_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098 -> T_IsDistributiveLattice_1012
d_isDistributiveLattice_1128 (T_DistributiveLattice_1098 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098
v0)))))
-- Relation.Binary.Lattice.DistributiveLattice._.isJoinSemilattice
d_isJoinSemilattice_1148 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1098 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_1148 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_DistributiveLattice_1098
-> T_IsJoinSemilattice_68
d_isJoinSemilattice_1148 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_DistributiveLattice_1098
v3
  = T_DistributiveLattice_1098 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_1148 T_DistributiveLattice_1098
v3
du_isJoinSemilattice_1148 ::
  T_DistributiveLattice_1098 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_1148 :: T_DistributiveLattice_1098 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_1148 T_DistributiveLattice_1098
v0
  = let v1 :: t
v1 = (T_DistributiveLattice_1098 -> T_Lattice_898) -> AgdaAny -> t
forall a b. a -> b
coe T_DistributiveLattice_1098 -> T_Lattice_898
du_lattice_1138 (T_DistributiveLattice_1098 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098
v0) in
    AgdaAny -> T_IsJoinSemilattice_68
forall a b. a -> b
coe ((T_IsLattice_810 -> T_IsJoinSemilattice_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 ((T_Lattice_898 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Relation.Binary.Lattice.DistributiveLattice._.isLattice
d_isLattice_1150 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1098 -> T_IsLattice_810
d_isLattice_1150 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_DistributiveLattice_1098
-> T_IsLattice_810
d_isLattice_1150 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_DistributiveLattice_1098
v3 = T_DistributiveLattice_1098 -> T_IsLattice_810
du_isLattice_1150 T_DistributiveLattice_1098
v3
du_isLattice_1150 :: T_DistributiveLattice_1098 -> T_IsLattice_810
du_isLattice_1150 :: T_DistributiveLattice_1098 -> T_IsLattice_810
du_isLattice_1150 T_DistributiveLattice_1098
v0
  = (T_IsDistributiveLattice_1012 -> T_IsLattice_810)
-> AgdaAny -> T_IsLattice_810
forall a b. a -> b
coe T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 ((T_DistributiveLattice_1098 -> T_IsDistributiveLattice_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098 -> T_IsDistributiveLattice_1012
d_isDistributiveLattice_1128 (T_DistributiveLattice_1098 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098
v0))
-- Relation.Binary.Lattice.DistributiveLattice._.isMeetSemilattice
d_isMeetSemilattice_1152 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1098 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_1152 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_DistributiveLattice_1098
-> T_IsMeetSemilattice_438
d_isMeetSemilattice_1152 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_DistributiveLattice_1098
v3
  = T_DistributiveLattice_1098 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_1152 T_DistributiveLattice_1098
v3
du_isMeetSemilattice_1152 ::
  T_DistributiveLattice_1098 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_1152 :: T_DistributiveLattice_1098 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_1152 T_DistributiveLattice_1098
v0
  = let v1 :: t
v1 = (T_DistributiveLattice_1098 -> T_Lattice_898) -> AgdaAny -> t
forall a b. a -> b
coe T_DistributiveLattice_1098 -> T_Lattice_898
du_lattice_1138 (T_DistributiveLattice_1098 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098
v0) in
    AgdaAny -> T_IsMeetSemilattice_438
forall a b. a -> b
coe ((T_IsLattice_810 -> T_IsMeetSemilattice_438) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 ((T_Lattice_898 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Relation.Binary.Lattice.DistributiveLattice._.isPartialOrder
d_isPartialOrder_1154 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1098 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_162
d_isPartialOrder_1154 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_DistributiveLattice_1098
-> T_IsPartialOrder_162
d_isPartialOrder_1154 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_DistributiveLattice_1098
v3 = T_DistributiveLattice_1098 -> T_IsPartialOrder_162
du_isPartialOrder_1154 T_DistributiveLattice_1098
v3
du_isPartialOrder_1154 ::
  T_DistributiveLattice_1098 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_162
du_isPartialOrder_1154 :: T_DistributiveLattice_1098 -> T_IsPartialOrder_162
du_isPartialOrder_1154 T_DistributiveLattice_1098
v0
  = (T_IsLattice_810 -> T_IsPartialOrder_162)
-> AgdaAny -> T_IsPartialOrder_162
forall a b. a -> b
coe
      T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
      ((T_IsDistributiveLattice_1012 -> T_IsLattice_810)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 ((T_DistributiveLattice_1098 -> T_IsDistributiveLattice_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098 -> T_IsDistributiveLattice_1012
d_isDistributiveLattice_1128 (T_DistributiveLattice_1098 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098
v0)))
-- Relation.Binary.Lattice.DistributiveLattice._.isPreorder
d_isPreorder_1156 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1098 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_1156 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_DistributiveLattice_1098
-> T_IsPreorder_70
d_isPreorder_1156 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_DistributiveLattice_1098
v3 = T_DistributiveLattice_1098 -> T_IsPreorder_70
du_isPreorder_1156 T_DistributiveLattice_1098
v3
du_isPreorder_1156 ::
  T_DistributiveLattice_1098 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
du_isPreorder_1156 :: T_DistributiveLattice_1098 -> T_IsPreorder_70
du_isPreorder_1156 T_DistributiveLattice_1098
v0
  = (T_IsPartialOrder_162 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
      ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
         ((T_IsDistributiveLattice_1012 -> T_IsLattice_810)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 ((T_DistributiveLattice_1098 -> T_IsDistributiveLattice_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098 -> T_IsDistributiveLattice_1012
d_isDistributiveLattice_1128 (T_DistributiveLattice_1098 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098
v0))))
-- Relation.Binary.Lattice.DistributiveLattice._.joinSemilattice
d_joinSemilattice_1158 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1098 -> T_JoinSemilattice_170
d_joinSemilattice_1158 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_DistributiveLattice_1098
-> T_JoinSemilattice_170
d_joinSemilattice_1158 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_DistributiveLattice_1098
v3 = T_DistributiveLattice_1098 -> T_JoinSemilattice_170
du_joinSemilattice_1158 T_DistributiveLattice_1098
v3
du_joinSemilattice_1158 ::
  T_DistributiveLattice_1098 -> T_JoinSemilattice_170
du_joinSemilattice_1158 :: T_DistributiveLattice_1098 -> T_JoinSemilattice_170
du_joinSemilattice_1158 T_DistributiveLattice_1098
v0
  = (T_Lattice_898 -> T_JoinSemilattice_170)
-> AgdaAny -> T_JoinSemilattice_170
forall a b. a -> b
coe T_Lattice_898 -> T_JoinSemilattice_170
du_joinSemilattice_986 ((T_DistributiveLattice_1098 -> T_Lattice_898) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098 -> T_Lattice_898
du_lattice_1138 (T_DistributiveLattice_1098 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098
v0))
-- Relation.Binary.Lattice.DistributiveLattice._.meetSemilattice
d_meetSemilattice_1160 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1098 -> T_MeetSemilattice_540
d_meetSemilattice_1160 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_DistributiveLattice_1098
-> T_MeetSemilattice_540
d_meetSemilattice_1160 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_DistributiveLattice_1098
v3 = T_DistributiveLattice_1098 -> T_MeetSemilattice_540
du_meetSemilattice_1160 T_DistributiveLattice_1098
v3
du_meetSemilattice_1160 ::
  T_DistributiveLattice_1098 -> T_MeetSemilattice_540
du_meetSemilattice_1160 :: T_DistributiveLattice_1098 -> T_MeetSemilattice_540
du_meetSemilattice_1160 T_DistributiveLattice_1098
v0
  = (T_Lattice_898 -> T_MeetSemilattice_540)
-> AgdaAny -> T_MeetSemilattice_540
forall a b. a -> b
coe T_Lattice_898 -> T_MeetSemilattice_540
du_meetSemilattice_988 ((T_DistributiveLattice_1098 -> T_Lattice_898) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098 -> T_Lattice_898
du_lattice_1138 (T_DistributiveLattice_1098 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098
v0))
-- Relation.Binary.Lattice.DistributiveLattice._.poset
d_poset_1162 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1098 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Poset_282
d_poset_1162 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_DistributiveLattice_1098
-> T_Poset_282
d_poset_1162 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_DistributiveLattice_1098
v3 = T_DistributiveLattice_1098 -> T_Poset_282
du_poset_1162 T_DistributiveLattice_1098
v3
du_poset_1162 ::
  T_DistributiveLattice_1098 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Poset_282
du_poset_1162 :: T_DistributiveLattice_1098 -> T_Poset_282
du_poset_1162 T_DistributiveLattice_1098
v0
  = let v1 :: t
v1 = (T_DistributiveLattice_1098 -> T_Lattice_898) -> AgdaAny -> t
forall a b. a -> b
coe T_DistributiveLattice_1098 -> T_Lattice_898
du_lattice_1138 (T_DistributiveLattice_1098 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098
v0) in
    AgdaAny -> T_Poset_282
forall a b. a -> b
coe ((T_JoinSemilattice_170 -> T_Poset_282) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_170 -> T_Poset_282
du_poset_240 ((T_Lattice_898 -> T_JoinSemilattice_170) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_898 -> T_JoinSemilattice_170
du_joinSemilattice_986 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Relation.Binary.Lattice.DistributiveLattice._.preorder
d_preorder_1164 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1098 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Preorder_132
d_preorder_1164 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_DistributiveLattice_1098
-> T_Preorder_132
d_preorder_1164 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_DistributiveLattice_1098
v3 = T_DistributiveLattice_1098 -> T_Preorder_132
du_preorder_1164 T_DistributiveLattice_1098
v3
du_preorder_1164 ::
  T_DistributiveLattice_1098 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Preorder_132
du_preorder_1164 :: T_DistributiveLattice_1098 -> T_Preorder_132
du_preorder_1164 T_DistributiveLattice_1098
v0
  = let v1 :: t
v1 = (T_DistributiveLattice_1098 -> T_Lattice_898) -> AgdaAny -> t
forall a b. a -> b
coe T_DistributiveLattice_1098 -> T_Lattice_898
du_lattice_1138 (T_DistributiveLattice_1098 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098
v0) in
    AgdaAny -> T_Preorder_132
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Lattice_898 -> T_JoinSemilattice_170) -> AgdaAny -> t
forall a b. a -> b
coe T_Lattice_898 -> T_JoinSemilattice_170
du_joinSemilattice_986 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Poset_282 -> T_Preorder_132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Poset_282 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_326
            ((T_JoinSemilattice_170 -> T_Poset_282) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_170 -> T_Poset_282
du_poset_240 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Relation.Binary.Lattice.DistributiveLattice._.refl
d_refl_1166 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1098 -> AgdaAny -> AgdaAny
d_refl_1166 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_DistributiveLattice_1098
-> AgdaAny
-> AgdaAny
d_refl_1166 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_DistributiveLattice_1098
v3 = T_DistributiveLattice_1098 -> AgdaAny -> AgdaAny
du_refl_1166 T_DistributiveLattice_1098
v3
du_refl_1166 :: T_DistributiveLattice_1098 -> AgdaAny -> AgdaAny
du_refl_1166 :: T_DistributiveLattice_1098 -> AgdaAny -> AgdaAny
du_refl_1166 T_DistributiveLattice_1098
v0
  = let v1 :: t
v1 = (T_DistributiveLattice_1098 -> T_Lattice_898) -> AgdaAny -> t
forall a b. a -> b
coe T_DistributiveLattice_1098 -> T_Lattice_898
du_lattice_1138 (T_DistributiveLattice_1098 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_810
v2 = T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (AgdaAny -> T_Lattice_898
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsPreorder_70 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_70 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_98
               ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                  (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v3)))))
-- Relation.Binary.Lattice.DistributiveLattice._.reflexive
d_reflexive_1168 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1098 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_1168 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_DistributiveLattice_1098
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_reflexive_1168 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_DistributiveLattice_1098
v3 = T_DistributiveLattice_1098
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_reflexive_1168 T_DistributiveLattice_1098
v3
du_reflexive_1168 ::
  T_DistributiveLattice_1098 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_reflexive_1168 :: T_DistributiveLattice_1098
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_reflexive_1168 T_DistributiveLattice_1098
v0
  = (T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
            ((T_IsDistributiveLattice_1012 -> T_IsLattice_810)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 ((T_DistributiveLattice_1098 -> T_IsDistributiveLattice_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098 -> T_IsDistributiveLattice_1012
d_isDistributiveLattice_1128 (T_DistributiveLattice_1098 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098
v0)))))
-- Relation.Binary.Lattice.DistributiveLattice._.setoid
d_setoid_1170 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1098 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1170 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_DistributiveLattice_1098
-> T_Setoid_44
d_setoid_1170 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_DistributiveLattice_1098
v3 = T_DistributiveLattice_1098 -> T_Setoid_44
du_setoid_1170 T_DistributiveLattice_1098
v3
du_setoid_1170 ::
  T_DistributiveLattice_1098 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1170 :: T_DistributiveLattice_1098 -> T_Setoid_44
du_setoid_1170 T_DistributiveLattice_1098
v0
  = (T_Lattice_898 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe T_Lattice_898 -> T_Setoid_44
du_setoid_984 ((T_DistributiveLattice_1098 -> T_Lattice_898) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098 -> T_Lattice_898
du_lattice_1138 (T_DistributiveLattice_1098 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098
v0))
-- Relation.Binary.Lattice.DistributiveLattice._.supremum
d_supremum_1172 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1098 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_supremum_1172 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_DistributiveLattice_1098
-> AgdaAny
-> AgdaAny
-> T_Σ_14
d_supremum_1172 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_DistributiveLattice_1098
v3 = T_DistributiveLattice_1098 -> AgdaAny -> AgdaAny -> T_Σ_14
du_supremum_1172 T_DistributiveLattice_1098
v3
du_supremum_1172 ::
  T_DistributiveLattice_1098 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_supremum_1172 :: T_DistributiveLattice_1098 -> AgdaAny -> AgdaAny -> T_Σ_14
du_supremum_1172 T_DistributiveLattice_1098
v0
  = (T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_836
      ((T_IsDistributiveLattice_1012 -> T_IsLattice_810)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 ((T_DistributiveLattice_1098 -> T_IsDistributiveLattice_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098 -> T_IsDistributiveLattice_1012
d_isDistributiveLattice_1128 (T_DistributiveLattice_1098 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098
v0)))
-- Relation.Binary.Lattice.DistributiveLattice._.trans
d_trans_1174 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1098 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1174 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_DistributiveLattice_1098
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_1174 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_DistributiveLattice_1098
v3 = T_DistributiveLattice_1098
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1174 T_DistributiveLattice_1098
v3
du_trans_1174 ::
  T_DistributiveLattice_1098 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1174 :: T_DistributiveLattice_1098
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1174 T_DistributiveLattice_1098
v0
  = (T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
            ((T_IsDistributiveLattice_1012 -> T_IsLattice_810)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 ((T_DistributiveLattice_1098 -> T_IsDistributiveLattice_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098 -> T_IsDistributiveLattice_1012
d_isDistributiveLattice_1128 (T_DistributiveLattice_1098 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098
v0)))))
-- Relation.Binary.Lattice.DistributiveLattice._.x∧y≤x
d_x'8743'y'8804'x_1176 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1098 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'x_1176 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_DistributiveLattice_1098
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'x_1176 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_DistributiveLattice_1098
v3 = T_DistributiveLattice_1098 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_1176 T_DistributiveLattice_1098
v3
du_x'8743'y'8804'x_1176 ::
  T_DistributiveLattice_1098 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_1176 :: T_DistributiveLattice_1098 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_1176 T_DistributiveLattice_1098
v0
  = let v1 :: t
v1 = (T_DistributiveLattice_1098 -> T_Lattice_898) -> AgdaAny -> t
forall a b. a -> b
coe T_DistributiveLattice_1098 -> T_Lattice_898
du_lattice_1138 (T_DistributiveLattice_1098 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_810
v2 = T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (AgdaAny -> T_Lattice_898
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_466 ((T_IsLattice_810 -> T_IsMeetSemilattice_438) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v2))))
-- Relation.Binary.Lattice.DistributiveLattice._.x∧y≤y
d_x'8743'y'8804'y_1178 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1098 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'y_1178 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_DistributiveLattice_1098
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'y_1178 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_DistributiveLattice_1098
v3 = T_DistributiveLattice_1098 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_1178 T_DistributiveLattice_1098
v3
du_x'8743'y'8804'y_1178 ::
  T_DistributiveLattice_1098 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_1178 :: T_DistributiveLattice_1098 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_1178 T_DistributiveLattice_1098
v0
  = let v1 :: t
v1 = (T_DistributiveLattice_1098 -> T_Lattice_898) -> AgdaAny -> t
forall a b. a -> b
coe T_DistributiveLattice_1098 -> T_Lattice_898
du_lattice_1138 (T_DistributiveLattice_1098 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_810
v2 = T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (AgdaAny -> T_Lattice_898
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_478 ((T_IsLattice_810 -> T_IsMeetSemilattice_438) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v2))))
-- Relation.Binary.Lattice.DistributiveLattice._.x≤x∨y
d_x'8804'x'8744'y_1180 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1098 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8804'x'8744'y_1180 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_DistributiveLattice_1098
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8804'x'8744'y_1180 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_DistributiveLattice_1098
v3 = T_DistributiveLattice_1098 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_1180 T_DistributiveLattice_1098
v3
du_x'8804'x'8744'y_1180 ::
  T_DistributiveLattice_1098 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_1180 :: T_DistributiveLattice_1098 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_1180 T_DistributiveLattice_1098
v0
  = let v1 :: t
v1 = (T_DistributiveLattice_1098 -> T_Lattice_898) -> AgdaAny -> t
forall a b. a -> b
coe T_DistributiveLattice_1098 -> T_Lattice_898
du_lattice_1138 (T_DistributiveLattice_1098 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_810
v2 = T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (AgdaAny -> T_Lattice_898
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_96 ((T_IsLattice_810 -> T_IsJoinSemilattice_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v2))))
-- Relation.Binary.Lattice.DistributiveLattice._.y≤x∨y
d_y'8804'x'8744'y_1182 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1098 -> AgdaAny -> AgdaAny -> AgdaAny
d_y'8804'x'8744'y_1182 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_DistributiveLattice_1098
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_y'8804'x'8744'y_1182 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_DistributiveLattice_1098
v3 = T_DistributiveLattice_1098 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_1182 T_DistributiveLattice_1098
v3
du_y'8804'x'8744'y_1182 ::
  T_DistributiveLattice_1098 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_1182 :: T_DistributiveLattice_1098 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_1182 T_DistributiveLattice_1098
v0
  = let v1 :: t
v1 = (T_DistributiveLattice_1098 -> T_Lattice_898) -> AgdaAny -> t
forall a b. a -> b
coe T_DistributiveLattice_1098 -> T_Lattice_898
du_lattice_1138 (T_DistributiveLattice_1098 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_810
v2 = T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (AgdaAny -> T_Lattice_898
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_108 ((T_IsLattice_810 -> T_IsJoinSemilattice_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v2))))
-- Relation.Binary.Lattice.DistributiveLattice._.∧-greatest
d_'8743''45'greatest_1184 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1098 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'greatest_1184 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_DistributiveLattice_1098
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'greatest_1184 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_DistributiveLattice_1098
v3
  = T_DistributiveLattice_1098
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_1184 T_DistributiveLattice_1098
v3
du_'8743''45'greatest_1184 ::
  T_DistributiveLattice_1098 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_1184 :: T_DistributiveLattice_1098
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_1184 T_DistributiveLattice_1098
v0
  = let v1 :: t
v1 = (T_DistributiveLattice_1098 -> T_Lattice_898) -> AgdaAny -> t
forall a b. a -> b
coe T_DistributiveLattice_1098 -> T_Lattice_898
du_lattice_1138 (T_DistributiveLattice_1098 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_810
v2 = T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (AgdaAny -> T_Lattice_898
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMeetSemilattice_438
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMeetSemilattice_438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_492 ((T_IsLattice_810 -> T_IsMeetSemilattice_438) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v2))))
-- Relation.Binary.Lattice.DistributiveLattice._.∨-least
d_'8744''45'least_1186 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1098 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'least_1186 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_DistributiveLattice_1098
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'least_1186 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_DistributiveLattice_1098
v3 = T_DistributiveLattice_1098
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_1186 T_DistributiveLattice_1098
v3
du_'8744''45'least_1186 ::
  T_DistributiveLattice_1098 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_1186 :: T_DistributiveLattice_1098
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_1186 T_DistributiveLattice_1098
v0
  = let v1 :: t
v1 = (T_DistributiveLattice_1098 -> T_Lattice_898) -> AgdaAny -> t
forall a b. a -> b
coe T_DistributiveLattice_1098 -> T_Lattice_898
du_lattice_1138 (T_DistributiveLattice_1098 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_810
v2 = T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (AgdaAny -> T_Lattice_898
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsJoinSemilattice_68
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsJoinSemilattice_68
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_122 ((T_IsLattice_810 -> T_IsJoinSemilattice_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v2))))
-- Relation.Binary.Lattice.DistributiveLattice._.∼-resp-≈
d_'8764''45'resp'45''8776'_1188 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1098 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_1188 :: T_Level_18
-> T_Level_18 -> T_Level_18 -> T_DistributiveLattice_1098 -> T_Σ_14
d_'8764''45'resp'45''8776'_1188 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_DistributiveLattice_1098
v3
  = T_DistributiveLattice_1098 -> T_Σ_14
du_'8764''45'resp'45''8776'_1188 T_DistributiveLattice_1098
v3
du_'8764''45'resp'45''8776'_1188 ::
  T_DistributiveLattice_1098 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_1188 :: T_DistributiveLattice_1098 -> T_Σ_14
du_'8764''45'resp'45''8776'_1188 T_DistributiveLattice_1098
v0
  = let v1 :: t
v1 = (T_DistributiveLattice_1098 -> T_Lattice_898) -> AgdaAny -> t
forall a b. a -> b
coe T_DistributiveLattice_1098 -> T_Lattice_898
du_lattice_1138 (T_DistributiveLattice_1098 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_810
v2 = T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (AgdaAny -> T_Lattice_898
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsPreorder_70 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_70 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_112
               ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                  (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v3)))))
-- Relation.Binary.Lattice.DistributiveLattice._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_1190 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1098 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_1190 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_DistributiveLattice_1098
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_1190 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_DistributiveLattice_1098
v3
  = T_DistributiveLattice_1098
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_1190 T_DistributiveLattice_1098
v3
du_'8764''45'resp'691''45''8776'_1190 ::
  T_DistributiveLattice_1098 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_1190 :: T_DistributiveLattice_1098
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_1190 T_DistributiveLattice_1098
v0
  = let v1 :: t
v1 = (T_DistributiveLattice_1098 -> T_Lattice_898) -> AgdaAny -> t
forall a b. a -> b
coe T_DistributiveLattice_1098 -> T_Lattice_898
du_lattice_1138 (T_DistributiveLattice_1098 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_810
v2 = T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (AgdaAny -> T_Lattice_898
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_106
               ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                  (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v3)))))
-- Relation.Binary.Lattice.DistributiveLattice._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_1192 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1098 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_1192 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_DistributiveLattice_1098
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_1192 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_DistributiveLattice_1098
v3
  = T_DistributiveLattice_1098
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_1192 T_DistributiveLattice_1098
v3
du_'8764''45'resp'737''45''8776'_1192 ::
  T_DistributiveLattice_1098 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_1192 :: T_DistributiveLattice_1098
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_1192 T_DistributiveLattice_1098
v0
  = let v1 :: t
v1 = (T_DistributiveLattice_1098 -> T_Lattice_898) -> AgdaAny -> t
forall a b. a -> b
coe T_DistributiveLattice_1098 -> T_Lattice_898
du_lattice_1138 (T_DistributiveLattice_1098 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_810
v2 = T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (AgdaAny -> T_Lattice_898
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_100
               ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                  (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v3)))))
-- Relation.Binary.Lattice.DistributiveLattice._.Eq.isPartialEquivalence
d_isPartialEquivalence_1196 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1098 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1196 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_DistributiveLattice_1098
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1196 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_DistributiveLattice_1098
v3
  = T_DistributiveLattice_1098 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1196 T_DistributiveLattice_1098
v3
du_isPartialEquivalence_1196 ::
  T_DistributiveLattice_1098 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1196 :: T_DistributiveLattice_1098 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1196 T_DistributiveLattice_1098
v0
  = let v1 :: t
v1 = (T_DistributiveLattice_1098 -> T_Lattice_898) -> AgdaAny -> t
forall a b. a -> b
coe T_DistributiveLattice_1098 -> T_Lattice_898
du_lattice_1138 (T_DistributiveLattice_1098 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_810
v2 = T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (AgdaAny -> T_Lattice_898
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreorder_70
v4
                   = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                       (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                     (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v4))))))
-- Relation.Binary.Lattice.DistributiveLattice._.Eq.refl
d_refl_1198 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1098 -> AgdaAny -> AgdaAny
d_refl_1198 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_DistributiveLattice_1098
-> AgdaAny
-> AgdaAny
d_refl_1198 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_DistributiveLattice_1098
v3 = T_DistributiveLattice_1098 -> AgdaAny -> AgdaAny
du_refl_1198 T_DistributiveLattice_1098
v3
du_refl_1198 :: T_DistributiveLattice_1098 -> AgdaAny -> AgdaAny
du_refl_1198 :: T_DistributiveLattice_1098 -> AgdaAny -> AgdaAny
du_refl_1198 T_DistributiveLattice_1098
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
               ((T_IsDistributiveLattice_1012 -> T_IsLattice_810)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 ((T_DistributiveLattice_1098 -> T_IsDistributiveLattice_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098 -> T_IsDistributiveLattice_1012
d_isDistributiveLattice_1128 (T_DistributiveLattice_1098 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098
v0))))))
-- Relation.Binary.Lattice.DistributiveLattice._.Eq.reflexive
d_reflexive_1200 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1098 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1200 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_DistributiveLattice_1098
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1200 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_DistributiveLattice_1098
v3 = T_DistributiveLattice_1098
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1200 T_DistributiveLattice_1098
v3
du_reflexive_1200 ::
  T_DistributiveLattice_1098 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1200 :: T_DistributiveLattice_1098
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1200 T_DistributiveLattice_1098
v0
  = let v1 :: t
v1 = (T_DistributiveLattice_1098 -> T_Lattice_898) -> AgdaAny -> t
forall a b. a -> b
coe T_DistributiveLattice_1098 -> T_Lattice_898
du_lattice_1138 (T_DistributiveLattice_1098 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_810
v2 = T_Lattice_898 -> T_IsLattice_810
d_isLattice_928 (AgdaAny -> T_Lattice_898
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreorder_70
v4
                   = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                       (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                       (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v4))
                    AgdaAny
v5))))
-- Relation.Binary.Lattice.DistributiveLattice._.Eq.sym
d_sym_1202 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1098 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1202 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_DistributiveLattice_1098
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_1202 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_DistributiveLattice_1098
v3 = T_DistributiveLattice_1098
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1202 T_DistributiveLattice_1098
v3
du_sym_1202 ::
  T_DistributiveLattice_1098 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1202 :: T_DistributiveLattice_1098
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1202 T_DistributiveLattice_1098
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
               ((T_IsDistributiveLattice_1012 -> T_IsLattice_810)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 ((T_DistributiveLattice_1098 -> T_IsDistributiveLattice_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098 -> T_IsDistributiveLattice_1012
d_isDistributiveLattice_1128 (T_DistributiveLattice_1098 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098
v0))))))
-- Relation.Binary.Lattice.DistributiveLattice._.Eq.trans
d_trans_1204 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_DistributiveLattice_1098 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1204 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_DistributiveLattice_1098
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_1204 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_DistributiveLattice_1098
v3 = T_DistributiveLattice_1098
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1204 T_DistributiveLattice_1098
v3
du_trans_1204 ::
  T_DistributiveLattice_1098 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1204 :: T_DistributiveLattice_1098
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1204 T_DistributiveLattice_1098
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
               ((T_IsDistributiveLattice_1012 -> T_IsLattice_810)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsDistributiveLattice_1012 -> T_IsLattice_810
d_isLattice_1034 ((T_DistributiveLattice_1098 -> T_IsDistributiveLattice_1012)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098 -> T_IsDistributiveLattice_1012
d_isDistributiveLattice_1128 (T_DistributiveLattice_1098 -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_1098
v0))))))
-- Relation.Binary.Lattice.IsBoundedLattice
d_IsBoundedLattice_1226 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsBoundedLattice_1226 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 p
a9 = ()
data T_IsBoundedLattice_1226
  = C_IsBoundedLattice'46'constructor_39749 T_IsLattice_810
                                            (AgdaAny -> AgdaAny) (AgdaAny -> AgdaAny)
-- Relation.Binary.Lattice.IsBoundedLattice.isLattice
d_isLattice_1254 :: T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 :: T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 T_IsBoundedLattice_1226
v0
  = case T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v0 of
      C_IsBoundedLattice'46'constructor_39749 T_IsLattice_810
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 -> T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v1
      T_IsBoundedLattice_1226
_ -> T_IsLattice_810
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.IsBoundedLattice.maximum
d_maximum_1256 :: T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny
d_maximum_1256 :: T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny
d_maximum_1256 T_IsBoundedLattice_1226
v0
  = case T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v0 of
      C_IsBoundedLattice'46'constructor_39749 T_IsLattice_810
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_IsBoundedLattice_1226
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.IsBoundedLattice.minimum
d_minimum_1258 :: T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny
d_minimum_1258 :: T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny
d_minimum_1258 T_IsBoundedLattice_1226
v0
  = case T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v0 of
      C_IsBoundedLattice'46'constructor_39749 T_IsLattice_810
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v3
      T_IsBoundedLattice_1226
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.IsBoundedLattice._.antisym
d_antisym_1262 ::
  T_IsBoundedLattice_1226 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_1262 :: T_IsBoundedLattice_1226
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_1262 T_IsBoundedLattice_1226
v0
  = (T_IsPartialOrder_162
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_162
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_172
      ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226
v0)))
-- Relation.Binary.Lattice.IsBoundedLattice._.infimum
d_infimum_1264 ::
  T_IsBoundedLattice_1226 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_infimum_1264 :: T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_1264 T_IsBoundedLattice_1226
v0
  = (T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_838 ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226
v0))
-- Relation.Binary.Lattice.IsBoundedLattice._.isEquivalence
d_isEquivalence_1266 ::
  T_IsBoundedLattice_1226 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1266 :: T_IsBoundedLattice_1226 -> T_IsEquivalence_26
d_isEquivalence_1266 T_IsBoundedLattice_1226
v0
  = (T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226
v0))))
-- Relation.Binary.Lattice.IsBoundedLattice._.isJoinSemilattice
d_isJoinSemilattice_1268 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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_IsBoundedLattice_1226 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_1268 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_1226
-> T_IsJoinSemilattice_68
d_isJoinSemilattice_1268 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny
v8 ~AgdaAny
v9
                         T_IsBoundedLattice_1226
v10
  = T_IsBoundedLattice_1226 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_1268 T_IsBoundedLattice_1226
v10
du_isJoinSemilattice_1268 ::
  T_IsBoundedLattice_1226 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_1268 :: T_IsBoundedLattice_1226 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_1268 T_IsBoundedLattice_1226
v0
  = (T_IsLattice_810 -> T_IsJoinSemilattice_68)
-> AgdaAny -> T_IsJoinSemilattice_68
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226
v0))
-- Relation.Binary.Lattice.IsBoundedLattice._.isMeetSemilattice
d_isMeetSemilattice_1270 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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_IsBoundedLattice_1226 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_1270 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_1226
-> T_IsMeetSemilattice_438
d_isMeetSemilattice_1270 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny
v8 ~AgdaAny
v9
                         T_IsBoundedLattice_1226
v10
  = T_IsBoundedLattice_1226 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_1270 T_IsBoundedLattice_1226
v10
du_isMeetSemilattice_1270 ::
  T_IsBoundedLattice_1226 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_1270 :: T_IsBoundedLattice_1226 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_1270 T_IsBoundedLattice_1226
v0
  = (T_IsLattice_810 -> T_IsMeetSemilattice_438)
-> AgdaAny -> T_IsMeetSemilattice_438
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226
v0))
-- Relation.Binary.Lattice.IsBoundedLattice._.isPartialOrder
d_isPartialOrder_1272 ::
  T_IsBoundedLattice_1226 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_162
d_isPartialOrder_1272 :: T_IsBoundedLattice_1226 -> T_IsPartialOrder_162
d_isPartialOrder_1272 T_IsBoundedLattice_1226
v0
  = (T_IsLattice_810 -> T_IsPartialOrder_162)
-> AgdaAny -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226
v0))
-- Relation.Binary.Lattice.IsBoundedLattice._.isPreorder
d_isPreorder_1274 ::
  T_IsBoundedLattice_1226 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_1274 :: T_IsBoundedLattice_1226 -> T_IsPreorder_70
d_isPreorder_1274 T_IsBoundedLattice_1226
v0
  = (T_IsPartialOrder_162 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
      ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226
v0)))
-- Relation.Binary.Lattice.IsBoundedLattice._.refl
d_refl_1276 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny
d_refl_1276 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_1226
-> AgdaAny
-> AgdaAny
d_refl_1276 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny
v8 ~AgdaAny
v9 T_IsBoundedLattice_1226
v10
  = T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny
du_refl_1276 T_IsBoundedLattice_1226
v10
du_refl_1276 :: T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny
du_refl_1276 :: T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny
du_refl_1276 T_IsBoundedLattice_1226
v0
  = let v1 :: T_IsLattice_810
v1 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_70 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_98
            ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
               (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v2))))
-- Relation.Binary.Lattice.IsBoundedLattice._.reflexive
d_reflexive_1278 ::
  T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_1278 :: T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_1278 T_IsBoundedLattice_1226
v0
  = (T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226
v0))))
-- Relation.Binary.Lattice.IsBoundedLattice._.supremum
d_supremum_1280 ::
  T_IsBoundedLattice_1226 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_supremum_1280 :: T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_1280 T_IsBoundedLattice_1226
v0
  = (T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_836 ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226
v0))
-- Relation.Binary.Lattice.IsBoundedLattice._.trans
d_trans_1282 ::
  T_IsBoundedLattice_1226 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1282 :: T_IsBoundedLattice_1226
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1282 T_IsBoundedLattice_1226
v0
  = (T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226
v0))))
-- Relation.Binary.Lattice.IsBoundedLattice._.x∧y≤x
d_x'8743'y'8804'x_1284 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'x_1284 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_1226
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'x_1284 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny
v8 ~AgdaAny
v9 T_IsBoundedLattice_1226
v10
  = T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_1284 T_IsBoundedLattice_1226
v10
du_x'8743'y'8804'x_1284 ::
  T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_1284 :: T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_1284 T_IsBoundedLattice_1226
v0
  = let v1 :: T_IsLattice_810
v1 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_466 ((T_IsLattice_810 -> T_IsMeetSemilattice_438) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v1)))
-- Relation.Binary.Lattice.IsBoundedLattice._.x∧y≤y
d_x'8743'y'8804'y_1286 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'y_1286 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_1226
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'y_1286 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny
v8 ~AgdaAny
v9 T_IsBoundedLattice_1226
v10
  = T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_1286 T_IsBoundedLattice_1226
v10
du_x'8743'y'8804'y_1286 ::
  T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_1286 :: T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_1286 T_IsBoundedLattice_1226
v0
  = let v1 :: T_IsLattice_810
v1 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_478 ((T_IsLattice_810 -> T_IsMeetSemilattice_438) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v1)))
-- Relation.Binary.Lattice.IsBoundedLattice._.x≤x∨y
d_x'8804'x'8744'y_1288 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8804'x'8744'y_1288 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_1226
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8804'x'8744'y_1288 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny
v8 ~AgdaAny
v9 T_IsBoundedLattice_1226
v10
  = T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_1288 T_IsBoundedLattice_1226
v10
du_x'8804'x'8744'y_1288 ::
  T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_1288 :: T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_1288 T_IsBoundedLattice_1226
v0
  = let v1 :: T_IsLattice_810
v1 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_96 ((T_IsLattice_810 -> T_IsJoinSemilattice_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v1)))
-- Relation.Binary.Lattice.IsBoundedLattice._.y≤x∨y
d_y'8804'x'8744'y_1290 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny -> AgdaAny
d_y'8804'x'8744'y_1290 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_1226
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_y'8804'x'8744'y_1290 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny
v8 ~AgdaAny
v9 T_IsBoundedLattice_1226
v10
  = T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_1290 T_IsBoundedLattice_1226
v10
du_y'8804'x'8744'y_1290 ::
  T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_1290 :: T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_1290 T_IsBoundedLattice_1226
v0
  = let v1 :: T_IsLattice_810
v1 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_108 ((T_IsLattice_810 -> T_IsJoinSemilattice_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v1)))
-- Relation.Binary.Lattice.IsBoundedLattice._.∧-greatest
d_'8743''45'greatest_1292 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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_IsBoundedLattice_1226 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'greatest_1292 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_1226
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'greatest_1292 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny
v8 ~AgdaAny
v9
                          T_IsBoundedLattice_1226
v10
  = T_IsBoundedLattice_1226
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_1292 T_IsBoundedLattice_1226
v10
du_'8743''45'greatest_1292 ::
  T_IsBoundedLattice_1226 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_1292 :: T_IsBoundedLattice_1226
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_1292 T_IsBoundedLattice_1226
v0
  = let v1 :: T_IsLattice_810
v1 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMeetSemilattice_438
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMeetSemilattice_438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_492 ((T_IsLattice_810 -> T_IsMeetSemilattice_438) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v1)))
-- Relation.Binary.Lattice.IsBoundedLattice._.∨-least
d_'8744''45'least_1294 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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_IsBoundedLattice_1226 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'least_1294 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_1226
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'least_1294 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny
v8 ~AgdaAny
v9 T_IsBoundedLattice_1226
v10
  = T_IsBoundedLattice_1226
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_1294 T_IsBoundedLattice_1226
v10
du_'8744''45'least_1294 ::
  T_IsBoundedLattice_1226 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_1294 :: T_IsBoundedLattice_1226
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_1294 T_IsBoundedLattice_1226
v0
  = let v1 :: T_IsLattice_810
v1 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsJoinSemilattice_68
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsJoinSemilattice_68
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_122 ((T_IsLattice_810 -> T_IsJoinSemilattice_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v1)))
-- Relation.Binary.Lattice.IsBoundedLattice._.∼-resp-≈
d_'8764''45'resp'45''8776'_1296 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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_IsBoundedLattice_1226 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_1296 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_1226
-> T_Σ_14
d_'8764''45'resp'45''8776'_1296 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny
v8
                                ~AgdaAny
v9 T_IsBoundedLattice_1226
v10
  = T_IsBoundedLattice_1226 -> T_Σ_14
du_'8764''45'resp'45''8776'_1296 T_IsBoundedLattice_1226
v10
du_'8764''45'resp'45''8776'_1296 ::
  T_IsBoundedLattice_1226 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_1296 :: T_IsBoundedLattice_1226 -> T_Σ_14
du_'8764''45'resp'45''8776'_1296 T_IsBoundedLattice_1226
v0
  = let v1 :: T_IsLattice_810
v1 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_70 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_112
            ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
               (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v2))))
-- Relation.Binary.Lattice.IsBoundedLattice._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_1298 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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_IsBoundedLattice_1226 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_1298 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_1226
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_1298 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6
                                     ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny
v8 ~AgdaAny
v9 T_IsBoundedLattice_1226
v10
  = T_IsBoundedLattice_1226
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_1298 T_IsBoundedLattice_1226
v10
du_'8764''45'resp'691''45''8776'_1298 ::
  T_IsBoundedLattice_1226 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_1298 :: T_IsBoundedLattice_1226
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_1298 T_IsBoundedLattice_1226
v0
  = let v1 :: T_IsLattice_810
v1 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_106
            ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
               (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v2))))
-- Relation.Binary.Lattice.IsBoundedLattice._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_1300 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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_IsBoundedLattice_1226 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_1300 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_1226
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_1300 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6
                                     ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny
v8 ~AgdaAny
v9 T_IsBoundedLattice_1226
v10
  = T_IsBoundedLattice_1226
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_1300 T_IsBoundedLattice_1226
v10
du_'8764''45'resp'737''45''8776'_1300 ::
  T_IsBoundedLattice_1226 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_1300 :: T_IsBoundedLattice_1226
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_1300 T_IsBoundedLattice_1226
v0
  = let v1 :: T_IsLattice_810
v1 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_100
            ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
               (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v2))))
-- Relation.Binary.Lattice.IsBoundedLattice._.Eq.isPartialEquivalence
d_isPartialEquivalence_1304 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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_IsBoundedLattice_1226 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1304 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_1226
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1304 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny
v8 ~AgdaAny
v9
                            T_IsBoundedLattice_1226
v10
  = T_IsBoundedLattice_1226 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1304 T_IsBoundedLattice_1226
v10
du_isPartialEquivalence_1304 ::
  T_IsBoundedLattice_1226 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1304 :: T_IsBoundedLattice_1226 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1304 T_IsBoundedLattice_1226
v0
  = let v1 :: T_IsLattice_810
v1 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreorder_70
v3
                = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                    (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                  (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v3)))))
-- Relation.Binary.Lattice.IsBoundedLattice._.Eq.refl
d_refl_1306 :: T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny
d_refl_1306 :: T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny
d_refl_1306 T_IsBoundedLattice_1226
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226
v0)))))
-- Relation.Binary.Lattice.IsBoundedLattice._.Eq.reflexive
d_reflexive_1308 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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_IsBoundedLattice_1226 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1308 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_1226
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1308 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny
v8 ~AgdaAny
v9 T_IsBoundedLattice_1226
v10
  = T_IsBoundedLattice_1226
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1308 T_IsBoundedLattice_1226
v10
du_reflexive_1308 ::
  T_IsBoundedLattice_1226 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1308 :: T_IsBoundedLattice_1226
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1308 T_IsBoundedLattice_1226
v0
  = let v1 :: T_IsLattice_810
v1 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_162
v2 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreorder_70
v3
                = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                    (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                    (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v3))
                 AgdaAny
v4)))
-- Relation.Binary.Lattice.IsBoundedLattice._.Eq.sym
d_sym_1310 ::
  T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1310 :: T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1310 T_IsBoundedLattice_1226
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226
v0)))))
-- Relation.Binary.Lattice.IsBoundedLattice._.Eq.trans
d_trans_1312 ::
  T_IsBoundedLattice_1226 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1312 :: T_IsBoundedLattice_1226
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1312 T_IsBoundedLattice_1226
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226
v0)))))
-- Relation.Binary.Lattice.IsBoundedLattice.isBoundedJoinSemilattice
d_isBoundedJoinSemilattice_1314 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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_IsBoundedLattice_1226 -> T_IsBoundedJoinSemilattice_262
d_isBoundedJoinSemilattice_1314 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_1226
-> T_IsBoundedJoinSemilattice_262
d_isBoundedJoinSemilattice_1314 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny
v8
                                ~AgdaAny
v9 T_IsBoundedLattice_1226
v10
  = T_IsBoundedLattice_1226 -> T_IsBoundedJoinSemilattice_262
du_isBoundedJoinSemilattice_1314 T_IsBoundedLattice_1226
v10
du_isBoundedJoinSemilattice_1314 ::
  T_IsBoundedLattice_1226 -> T_IsBoundedJoinSemilattice_262
du_isBoundedJoinSemilattice_1314 :: T_IsBoundedLattice_1226 -> T_IsBoundedJoinSemilattice_262
du_isBoundedJoinSemilattice_1314 T_IsBoundedLattice_1226
v0
  = (T_IsJoinSemilattice_68
 -> (AgdaAny -> AgdaAny) -> T_IsBoundedJoinSemilattice_262)
-> AgdaAny -> AgdaAny -> T_IsBoundedJoinSemilattice_262
forall a b. a -> b
coe
      T_IsJoinSemilattice_68
-> (AgdaAny -> AgdaAny) -> T_IsBoundedJoinSemilattice_262
C_IsBoundedJoinSemilattice'46'constructor_9099
      ((T_IsLattice_810 -> T_IsJoinSemilattice_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226
v0)))
      ((T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny
d_minimum_1258 (T_IsBoundedLattice_1226 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226
v0))
-- Relation.Binary.Lattice.IsBoundedLattice.isBoundedMeetSemilattice
d_isBoundedMeetSemilattice_1316 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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_IsBoundedLattice_1226 -> T_IsBoundedMeetSemilattice_632
d_isBoundedMeetSemilattice_1316 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_1226
-> T_IsBoundedMeetSemilattice_632
d_isBoundedMeetSemilattice_1316 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny
v8
                                ~AgdaAny
v9 T_IsBoundedLattice_1226
v10
  = T_IsBoundedLattice_1226 -> T_IsBoundedMeetSemilattice_632
du_isBoundedMeetSemilattice_1316 T_IsBoundedLattice_1226
v10
du_isBoundedMeetSemilattice_1316 ::
  T_IsBoundedLattice_1226 -> T_IsBoundedMeetSemilattice_632
du_isBoundedMeetSemilattice_1316 :: T_IsBoundedLattice_1226 -> T_IsBoundedMeetSemilattice_632
du_isBoundedMeetSemilattice_1316 T_IsBoundedLattice_1226
v0
  = (T_IsMeetSemilattice_438
 -> (AgdaAny -> AgdaAny) -> T_IsBoundedMeetSemilattice_632)
-> AgdaAny -> AgdaAny -> T_IsBoundedMeetSemilattice_632
forall a b. a -> b
coe
      T_IsMeetSemilattice_438
-> (AgdaAny -> AgdaAny) -> T_IsBoundedMeetSemilattice_632
C_IsBoundedMeetSemilattice'46'constructor_20757
      ((T_IsLattice_810 -> T_IsMeetSemilattice_438) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226
v0)))
      ((T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny
d_maximum_1256 (T_IsBoundedLattice_1226 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226
v0))
-- Relation.Binary.Lattice.BoundedLattice
d_BoundedLattice_1324 :: p -> p -> p -> T_Level_18
d_BoundedLattice_1324 p
a0 p
a1 p
a2 = ()
data T_BoundedLattice_1324
  = C_BoundedLattice'46'constructor_44603 (AgdaAny ->
                                           AgdaAny -> AgdaAny)
                                          (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny AgdaAny
                                          T_IsBoundedLattice_1226
-- Relation.Binary.Lattice.BoundedLattice.Carrier
d_Carrier_1348 :: T_BoundedLattice_1324 -> ()
d_Carrier_1348 :: T_BoundedLattice_1324 -> T_Level_18
d_Carrier_1348 = T_BoundedLattice_1324 -> T_Level_18
forall a. a
erased
-- Relation.Binary.Lattice.BoundedLattice._≈_
d__'8776'__1350 ::
  T_BoundedLattice_1324 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1350 :: T_BoundedLattice_1324 -> AgdaAny -> AgdaAny -> T_Level_18
d__'8776'__1350 = T_BoundedLattice_1324 -> AgdaAny -> AgdaAny -> T_Level_18
forall a. a
erased
-- Relation.Binary.Lattice.BoundedLattice._≤_
d__'8804'__1352 ::
  T_BoundedLattice_1324 -> AgdaAny -> AgdaAny -> ()
d__'8804'__1352 :: T_BoundedLattice_1324 -> AgdaAny -> AgdaAny -> T_Level_18
d__'8804'__1352 = T_BoundedLattice_1324 -> AgdaAny -> AgdaAny -> T_Level_18
forall a. a
erased
-- Relation.Binary.Lattice.BoundedLattice._∨_
d__'8744'__1354 ::
  T_BoundedLattice_1324 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__1354 :: T_BoundedLattice_1324 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__1354 T_BoundedLattice_1324
v0
  = case T_BoundedLattice_1324 -> T_BoundedLattice_1324
forall a b. a -> b
coe T_BoundedLattice_1324
v0 of
      C_BoundedLattice'46'constructor_44603 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsBoundedLattice_1226
v8 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_BoundedLattice_1324
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.BoundedLattice._∧_
d__'8743'__1356 ::
  T_BoundedLattice_1324 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__1356 :: T_BoundedLattice_1324 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__1356 T_BoundedLattice_1324
v0
  = case T_BoundedLattice_1324 -> T_BoundedLattice_1324
forall a b. a -> b
coe T_BoundedLattice_1324
v0 of
      C_BoundedLattice'46'constructor_44603 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsBoundedLattice_1226
v8 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v5
      T_BoundedLattice_1324
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.BoundedLattice.⊤
d_'8868'_1358 :: T_BoundedLattice_1324 -> AgdaAny
d_'8868'_1358 :: T_BoundedLattice_1324 -> AgdaAny
d_'8868'_1358 T_BoundedLattice_1324
v0
  = case T_BoundedLattice_1324 -> T_BoundedLattice_1324
forall a b. a -> b
coe T_BoundedLattice_1324
v0 of
      C_BoundedLattice'46'constructor_44603 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsBoundedLattice_1226
v8 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v6
      T_BoundedLattice_1324
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.BoundedLattice.⊥
d_'8869'_1360 :: T_BoundedLattice_1324 -> AgdaAny
d_'8869'_1360 :: T_BoundedLattice_1324 -> AgdaAny
d_'8869'_1360 T_BoundedLattice_1324
v0
  = case T_BoundedLattice_1324 -> T_BoundedLattice_1324
forall a b. a -> b
coe T_BoundedLattice_1324
v0 of
      C_BoundedLattice'46'constructor_44603 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsBoundedLattice_1226
v8 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v7
      T_BoundedLattice_1324
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.BoundedLattice.isBoundedLattice
d_isBoundedLattice_1362 ::
  T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 :: T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 T_BoundedLattice_1324
v0
  = case T_BoundedLattice_1324 -> T_BoundedLattice_1324
forall a b. a -> b
coe T_BoundedLattice_1324
v0 of
      C_BoundedLattice'46'constructor_44603 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 T_IsBoundedLattice_1226
v8 -> T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v8
      T_BoundedLattice_1324
_ -> T_IsBoundedLattice_1226
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.BoundedLattice._.antisym
d_antisym_1366 ::
  T_BoundedLattice_1324 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_1366 :: T_BoundedLattice_1324
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_1366 T_BoundedLattice_1324
v0
  = (T_IsPartialOrder_162
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_162
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_172
      ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
         ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 ((T_BoundedLattice_1324 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (T_BoundedLattice_1324 -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324
v0))))
-- Relation.Binary.Lattice.BoundedLattice._.infimum
d_infimum_1368 ::
  T_BoundedLattice_1324 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_infimum_1368 :: T_BoundedLattice_1324 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_1368 T_BoundedLattice_1324
v0
  = (T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_838
      ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 ((T_BoundedLattice_1324 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (T_BoundedLattice_1324 -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324
v0)))
-- Relation.Binary.Lattice.BoundedLattice._.isBoundedJoinSemilattice
d_isBoundedJoinSemilattice_1370 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedLattice_1324 -> T_IsBoundedJoinSemilattice_262
d_isBoundedJoinSemilattice_1370 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedLattice_1324
-> T_IsBoundedJoinSemilattice_262
d_isBoundedJoinSemilattice_1370 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedLattice_1324
v3
  = T_BoundedLattice_1324 -> T_IsBoundedJoinSemilattice_262
du_isBoundedJoinSemilattice_1370 T_BoundedLattice_1324
v3
du_isBoundedJoinSemilattice_1370 ::
  T_BoundedLattice_1324 -> T_IsBoundedJoinSemilattice_262
du_isBoundedJoinSemilattice_1370 :: T_BoundedLattice_1324 -> T_IsBoundedJoinSemilattice_262
du_isBoundedJoinSemilattice_1370 T_BoundedLattice_1324
v0
  = (T_IsBoundedLattice_1226 -> T_IsBoundedJoinSemilattice_262)
-> AgdaAny -> T_IsBoundedJoinSemilattice_262
forall a b. a -> b
coe
      T_IsBoundedLattice_1226 -> T_IsBoundedJoinSemilattice_262
du_isBoundedJoinSemilattice_1314
      ((T_BoundedLattice_1324 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (T_BoundedLattice_1324 -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324
v0))
-- Relation.Binary.Lattice.BoundedLattice._.isBoundedMeetSemilattice
d_isBoundedMeetSemilattice_1372 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedLattice_1324 -> T_IsBoundedMeetSemilattice_632
d_isBoundedMeetSemilattice_1372 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedLattice_1324
-> T_IsBoundedMeetSemilattice_632
d_isBoundedMeetSemilattice_1372 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedLattice_1324
v3
  = T_BoundedLattice_1324 -> T_IsBoundedMeetSemilattice_632
du_isBoundedMeetSemilattice_1372 T_BoundedLattice_1324
v3
du_isBoundedMeetSemilattice_1372 ::
  T_BoundedLattice_1324 -> T_IsBoundedMeetSemilattice_632
du_isBoundedMeetSemilattice_1372 :: T_BoundedLattice_1324 -> T_IsBoundedMeetSemilattice_632
du_isBoundedMeetSemilattice_1372 T_BoundedLattice_1324
v0
  = (T_IsBoundedLattice_1226 -> T_IsBoundedMeetSemilattice_632)
-> AgdaAny -> T_IsBoundedMeetSemilattice_632
forall a b. a -> b
coe
      T_IsBoundedLattice_1226 -> T_IsBoundedMeetSemilattice_632
du_isBoundedMeetSemilattice_1316
      ((T_BoundedLattice_1324 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (T_BoundedLattice_1324 -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324
v0))
-- Relation.Binary.Lattice.BoundedLattice._.isEquivalence
d_isEquivalence_1374 ::
  T_BoundedLattice_1324 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1374 :: T_BoundedLattice_1324 -> T_IsEquivalence_26
d_isEquivalence_1374 T_BoundedLattice_1324
v0
  = (T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
            ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 ((T_BoundedLattice_1324 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (T_BoundedLattice_1324 -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324
v0)))))
-- Relation.Binary.Lattice.BoundedLattice._.isJoinSemilattice
d_isJoinSemilattice_1376 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedLattice_1324 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_1376 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedLattice_1324
-> T_IsJoinSemilattice_68
d_isJoinSemilattice_1376 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedLattice_1324
v3
  = T_BoundedLattice_1324 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_1376 T_BoundedLattice_1324
v3
du_isJoinSemilattice_1376 ::
  T_BoundedLattice_1324 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_1376 :: T_BoundedLattice_1324 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_1376 T_BoundedLattice_1324
v0
  = let v1 :: T_IsBoundedLattice_1226
v1 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (T_BoundedLattice_1324 -> T_BoundedLattice_1324
forall a b. a -> b
coe T_BoundedLattice_1324
v0) in
    AgdaAny -> T_IsJoinSemilattice_68
forall a b. a -> b
coe ((T_IsLattice_810 -> T_IsJoinSemilattice_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226
v1)))
-- Relation.Binary.Lattice.BoundedLattice._.isLattice
d_isLattice_1378 :: T_BoundedLattice_1324 -> T_IsLattice_810
d_isLattice_1378 :: T_BoundedLattice_1324 -> T_IsLattice_810
d_isLattice_1378 T_BoundedLattice_1324
v0
  = (T_IsBoundedLattice_1226 -> T_IsLattice_810)
-> AgdaAny -> T_IsLattice_810
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 ((T_BoundedLattice_1324 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (T_BoundedLattice_1324 -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324
v0))
-- Relation.Binary.Lattice.BoundedLattice._.isMeetSemilattice
d_isMeetSemilattice_1380 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedLattice_1324 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_1380 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedLattice_1324
-> T_IsMeetSemilattice_438
d_isMeetSemilattice_1380 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedLattice_1324
v3
  = T_BoundedLattice_1324 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_1380 T_BoundedLattice_1324
v3
du_isMeetSemilattice_1380 ::
  T_BoundedLattice_1324 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_1380 :: T_BoundedLattice_1324 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_1380 T_BoundedLattice_1324
v0
  = let v1 :: T_IsBoundedLattice_1226
v1 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (T_BoundedLattice_1324 -> T_BoundedLattice_1324
forall a b. a -> b
coe T_BoundedLattice_1324
v0) in
    AgdaAny -> T_IsMeetSemilattice_438
forall a b. a -> b
coe ((T_IsLattice_810 -> T_IsMeetSemilattice_438) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226
v1)))
-- Relation.Binary.Lattice.BoundedLattice._.isPartialOrder
d_isPartialOrder_1382 ::
  T_BoundedLattice_1324 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_162
d_isPartialOrder_1382 :: T_BoundedLattice_1324 -> T_IsPartialOrder_162
d_isPartialOrder_1382 T_BoundedLattice_1324
v0
  = (T_IsLattice_810 -> T_IsPartialOrder_162)
-> AgdaAny -> T_IsPartialOrder_162
forall a b. a -> b
coe
      T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
      ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 ((T_BoundedLattice_1324 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (T_BoundedLattice_1324 -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324
v0)))
-- Relation.Binary.Lattice.BoundedLattice._.isPreorder
d_isPreorder_1384 ::
  T_BoundedLattice_1324 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_1384 :: T_BoundedLattice_1324 -> T_IsPreorder_70
d_isPreorder_1384 T_BoundedLattice_1324
v0
  = (T_IsPartialOrder_162 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
      ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
         ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 ((T_BoundedLattice_1324 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (T_BoundedLattice_1324 -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324
v0))))
-- Relation.Binary.Lattice.BoundedLattice._.maximum
d_maximum_1386 :: T_BoundedLattice_1324 -> AgdaAny -> AgdaAny
d_maximum_1386 :: T_BoundedLattice_1324 -> AgdaAny -> AgdaAny
d_maximum_1386 T_BoundedLattice_1324
v0
  = (T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny
d_maximum_1256 ((T_BoundedLattice_1324 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (T_BoundedLattice_1324 -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324
v0))
-- Relation.Binary.Lattice.BoundedLattice._.minimum
d_minimum_1388 :: T_BoundedLattice_1324 -> AgdaAny -> AgdaAny
d_minimum_1388 :: T_BoundedLattice_1324 -> AgdaAny -> AgdaAny
d_minimum_1388 T_BoundedLattice_1324
v0
  = (T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny
d_minimum_1258 ((T_BoundedLattice_1324 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (T_BoundedLattice_1324 -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324
v0))
-- Relation.Binary.Lattice.BoundedLattice._.refl
d_refl_1390 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedLattice_1324 -> AgdaAny -> AgdaAny
d_refl_1390 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedLattice_1324
-> AgdaAny
-> AgdaAny
d_refl_1390 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedLattice_1324
v3 = T_BoundedLattice_1324 -> AgdaAny -> AgdaAny
du_refl_1390 T_BoundedLattice_1324
v3
du_refl_1390 :: T_BoundedLattice_1324 -> AgdaAny -> AgdaAny
du_refl_1390 :: T_BoundedLattice_1324 -> AgdaAny -> AgdaAny
du_refl_1390 T_BoundedLattice_1324
v0
  = let v1 :: T_IsBoundedLattice_1226
v1 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (T_BoundedLattice_1324 -> T_BoundedLattice_1324
forall a b. a -> b
coe T_BoundedLattice_1324
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_810
v2 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsPreorder_70 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_70 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_98
               ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                  (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v3)))))
-- Relation.Binary.Lattice.BoundedLattice._.reflexive
d_reflexive_1392 ::
  T_BoundedLattice_1324 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_1392 :: T_BoundedLattice_1324 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_1392 T_BoundedLattice_1324
v0
  = (T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
            ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 ((T_BoundedLattice_1324 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (T_BoundedLattice_1324 -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324
v0)))))
-- Relation.Binary.Lattice.BoundedLattice._.supremum
d_supremum_1394 ::
  T_BoundedLattice_1324 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_supremum_1394 :: T_BoundedLattice_1324 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_1394 T_BoundedLattice_1324
v0
  = (T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_836
      ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 ((T_BoundedLattice_1324 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (T_BoundedLattice_1324 -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324
v0)))
-- Relation.Binary.Lattice.BoundedLattice._.trans
d_trans_1396 ::
  T_BoundedLattice_1324 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1396 :: T_BoundedLattice_1324
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1396 T_BoundedLattice_1324
v0
  = (T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
            ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 ((T_BoundedLattice_1324 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (T_BoundedLattice_1324 -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324
v0)))))
-- Relation.Binary.Lattice.BoundedLattice._.x∧y≤x
d_x'8743'y'8804'x_1398 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedLattice_1324 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'x_1398 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedLattice_1324
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'x_1398 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedLattice_1324
v3 = T_BoundedLattice_1324 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_1398 T_BoundedLattice_1324
v3
du_x'8743'y'8804'x_1398 ::
  T_BoundedLattice_1324 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_1398 :: T_BoundedLattice_1324 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_1398 T_BoundedLattice_1324
v0
  = let v1 :: T_IsBoundedLattice_1226
v1 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (T_BoundedLattice_1324 -> T_BoundedLattice_1324
forall a b. a -> b
coe T_BoundedLattice_1324
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_810
v2 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_466 ((T_IsLattice_810 -> T_IsMeetSemilattice_438) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v2))))
-- Relation.Binary.Lattice.BoundedLattice._.x∧y≤y
d_x'8743'y'8804'y_1400 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedLattice_1324 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'y_1400 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedLattice_1324
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'y_1400 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedLattice_1324
v3 = T_BoundedLattice_1324 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_1400 T_BoundedLattice_1324
v3
du_x'8743'y'8804'y_1400 ::
  T_BoundedLattice_1324 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_1400 :: T_BoundedLattice_1324 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_1400 T_BoundedLattice_1324
v0
  = let v1 :: T_IsBoundedLattice_1226
v1 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (T_BoundedLattice_1324 -> T_BoundedLattice_1324
forall a b. a -> b
coe T_BoundedLattice_1324
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_810
v2 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_478 ((T_IsLattice_810 -> T_IsMeetSemilattice_438) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v2))))
-- Relation.Binary.Lattice.BoundedLattice._.x≤x∨y
d_x'8804'x'8744'y_1402 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedLattice_1324 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8804'x'8744'y_1402 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedLattice_1324
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8804'x'8744'y_1402 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedLattice_1324
v3 = T_BoundedLattice_1324 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_1402 T_BoundedLattice_1324
v3
du_x'8804'x'8744'y_1402 ::
  T_BoundedLattice_1324 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_1402 :: T_BoundedLattice_1324 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_1402 T_BoundedLattice_1324
v0
  = let v1 :: T_IsBoundedLattice_1226
v1 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (T_BoundedLattice_1324 -> T_BoundedLattice_1324
forall a b. a -> b
coe T_BoundedLattice_1324
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_810
v2 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_96 ((T_IsLattice_810 -> T_IsJoinSemilattice_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v2))))
-- Relation.Binary.Lattice.BoundedLattice._.y≤x∨y
d_y'8804'x'8744'y_1404 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedLattice_1324 -> AgdaAny -> AgdaAny -> AgdaAny
d_y'8804'x'8744'y_1404 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedLattice_1324
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_y'8804'x'8744'y_1404 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedLattice_1324
v3 = T_BoundedLattice_1324 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_1404 T_BoundedLattice_1324
v3
du_y'8804'x'8744'y_1404 ::
  T_BoundedLattice_1324 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_1404 :: T_BoundedLattice_1324 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_1404 T_BoundedLattice_1324
v0
  = let v1 :: T_IsBoundedLattice_1226
v1 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (T_BoundedLattice_1324 -> T_BoundedLattice_1324
forall a b. a -> b
coe T_BoundedLattice_1324
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_810
v2 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_108 ((T_IsLattice_810 -> T_IsJoinSemilattice_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v2))))
-- Relation.Binary.Lattice.BoundedLattice._.∧-greatest
d_'8743''45'greatest_1406 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedLattice_1324 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'greatest_1406 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedLattice_1324
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'greatest_1406 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedLattice_1324
v3
  = T_BoundedLattice_1324
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_1406 T_BoundedLattice_1324
v3
du_'8743''45'greatest_1406 ::
  T_BoundedLattice_1324 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_1406 :: T_BoundedLattice_1324
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_1406 T_BoundedLattice_1324
v0
  = let v1 :: T_IsBoundedLattice_1226
v1 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (T_BoundedLattice_1324 -> T_BoundedLattice_1324
forall a b. a -> b
coe T_BoundedLattice_1324
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_810
v2 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMeetSemilattice_438
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMeetSemilattice_438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_492 ((T_IsLattice_810 -> T_IsMeetSemilattice_438) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v2))))
-- Relation.Binary.Lattice.BoundedLattice._.∨-least
d_'8744''45'least_1408 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedLattice_1324 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'least_1408 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedLattice_1324
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'least_1408 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedLattice_1324
v3 = T_BoundedLattice_1324
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_1408 T_BoundedLattice_1324
v3
du_'8744''45'least_1408 ::
  T_BoundedLattice_1324 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_1408 :: T_BoundedLattice_1324
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_1408 T_BoundedLattice_1324
v0
  = let v1 :: T_IsBoundedLattice_1226
v1 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (T_BoundedLattice_1324 -> T_BoundedLattice_1324
forall a b. a -> b
coe T_BoundedLattice_1324
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_810
v2 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsJoinSemilattice_68
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsJoinSemilattice_68
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_122 ((T_IsLattice_810 -> T_IsJoinSemilattice_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v2))))
-- Relation.Binary.Lattice.BoundedLattice._.∼-resp-≈
d_'8764''45'resp'45''8776'_1410 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedLattice_1324 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_1410 :: T_Level_18
-> T_Level_18 -> T_Level_18 -> T_BoundedLattice_1324 -> T_Σ_14
d_'8764''45'resp'45''8776'_1410 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedLattice_1324
v3
  = T_BoundedLattice_1324 -> T_Σ_14
du_'8764''45'resp'45''8776'_1410 T_BoundedLattice_1324
v3
du_'8764''45'resp'45''8776'_1410 ::
  T_BoundedLattice_1324 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_1410 :: T_BoundedLattice_1324 -> T_Σ_14
du_'8764''45'resp'45''8776'_1410 T_BoundedLattice_1324
v0
  = let v1 :: T_IsBoundedLattice_1226
v1 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (T_BoundedLattice_1324 -> T_BoundedLattice_1324
forall a b. a -> b
coe T_BoundedLattice_1324
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_810
v2 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsPreorder_70 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_70 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_112
               ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                  (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v3)))))
-- Relation.Binary.Lattice.BoundedLattice._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_1412 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedLattice_1324 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_1412 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedLattice_1324
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_1412 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedLattice_1324
v3
  = T_BoundedLattice_1324
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_1412 T_BoundedLattice_1324
v3
du_'8764''45'resp'691''45''8776'_1412 ::
  T_BoundedLattice_1324 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_1412 :: T_BoundedLattice_1324
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_1412 T_BoundedLattice_1324
v0
  = let v1 :: T_IsBoundedLattice_1226
v1 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (T_BoundedLattice_1324 -> T_BoundedLattice_1324
forall a b. a -> b
coe T_BoundedLattice_1324
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_810
v2 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_106
               ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                  (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v3)))))
-- Relation.Binary.Lattice.BoundedLattice._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_1414 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedLattice_1324 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_1414 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedLattice_1324
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_1414 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedLattice_1324
v3
  = T_BoundedLattice_1324
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_1414 T_BoundedLattice_1324
v3
du_'8764''45'resp'737''45''8776'_1414 ::
  T_BoundedLattice_1324 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_1414 :: T_BoundedLattice_1324
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_1414 T_BoundedLattice_1324
v0
  = let v1 :: T_IsBoundedLattice_1226
v1 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (T_BoundedLattice_1324 -> T_BoundedLattice_1324
forall a b. a -> b
coe T_BoundedLattice_1324
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_810
v2 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_100
               ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                  (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v3)))))
-- Relation.Binary.Lattice.BoundedLattice._.Eq.isPartialEquivalence
d_isPartialEquivalence_1418 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedLattice_1324 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1418 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedLattice_1324
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1418 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedLattice_1324
v3
  = T_BoundedLattice_1324 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1418 T_BoundedLattice_1324
v3
du_isPartialEquivalence_1418 ::
  T_BoundedLattice_1324 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1418 :: T_BoundedLattice_1324 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1418 T_BoundedLattice_1324
v0
  = let v1 :: T_IsBoundedLattice_1226
v1 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (T_BoundedLattice_1324 -> T_BoundedLattice_1324
forall a b. a -> b
coe T_BoundedLattice_1324
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_810
v2 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreorder_70
v4
                   = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                       (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                     (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v4))))))
-- Relation.Binary.Lattice.BoundedLattice._.Eq.refl
d_refl_1420 :: T_BoundedLattice_1324 -> AgdaAny -> AgdaAny
d_refl_1420 :: T_BoundedLattice_1324 -> AgdaAny -> AgdaAny
d_refl_1420 T_BoundedLattice_1324
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
               ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 ((T_BoundedLattice_1324 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (T_BoundedLattice_1324 -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324
v0))))))
-- Relation.Binary.Lattice.BoundedLattice._.Eq.reflexive
d_reflexive_1422 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedLattice_1324 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1422 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedLattice_1324
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1422 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedLattice_1324
v3 = T_BoundedLattice_1324
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1422 T_BoundedLattice_1324
v3
du_reflexive_1422 ::
  T_BoundedLattice_1324 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1422 :: T_BoundedLattice_1324
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1422 T_BoundedLattice_1324
v0
  = let v1 :: T_IsBoundedLattice_1226
v1 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (T_BoundedLattice_1324 -> T_BoundedLattice_1324
forall a b. a -> b
coe T_BoundedLattice_1324
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_810
v2 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreorder_70
v4
                   = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                       (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                       (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v4))
                    AgdaAny
v5))))
-- Relation.Binary.Lattice.BoundedLattice._.Eq.sym
d_sym_1424 ::
  T_BoundedLattice_1324 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1424 :: T_BoundedLattice_1324 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1424 T_BoundedLattice_1324
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
               ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 ((T_BoundedLattice_1324 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (T_BoundedLattice_1324 -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324
v0))))))
-- Relation.Binary.Lattice.BoundedLattice._.Eq.trans
d_trans_1426 ::
  T_BoundedLattice_1324 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1426 :: T_BoundedLattice_1324
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1426 T_BoundedLattice_1324
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
               ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 ((T_BoundedLattice_1324 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (T_BoundedLattice_1324 -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324
v0))))))
-- Relation.Binary.Lattice.BoundedLattice.boundedJoinSemilattice
d_boundedJoinSemilattice_1428 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedLattice_1324 -> T_BoundedJoinSemilattice_336
d_boundedJoinSemilattice_1428 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedLattice_1324
-> T_BoundedJoinSemilattice_336
d_boundedJoinSemilattice_1428 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedLattice_1324
v3
  = T_BoundedLattice_1324 -> T_BoundedJoinSemilattice_336
du_boundedJoinSemilattice_1428 T_BoundedLattice_1324
v3
du_boundedJoinSemilattice_1428 ::
  T_BoundedLattice_1324 -> T_BoundedJoinSemilattice_336
du_boundedJoinSemilattice_1428 :: T_BoundedLattice_1324 -> T_BoundedJoinSemilattice_336
du_boundedJoinSemilattice_1428 T_BoundedLattice_1324
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsBoundedJoinSemilattice_262
 -> T_BoundedJoinSemilattice_336)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_BoundedJoinSemilattice_336
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedJoinSemilattice_262
-> T_BoundedJoinSemilattice_336
C_BoundedJoinSemilattice'46'constructor_11633
      (T_BoundedLattice_1324 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__1354 (T_BoundedLattice_1324 -> T_BoundedLattice_1324
forall a b. a -> b
coe T_BoundedLattice_1324
v0)) (T_BoundedLattice_1324 -> AgdaAny
d_'8869'_1360 (T_BoundedLattice_1324 -> T_BoundedLattice_1324
forall a b. a -> b
coe T_BoundedLattice_1324
v0))
      ((T_IsBoundedLattice_1226 -> T_IsBoundedJoinSemilattice_262)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBoundedLattice_1226 -> T_IsBoundedJoinSemilattice_262
du_isBoundedJoinSemilattice_1314
         ((T_BoundedLattice_1324 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (T_BoundedLattice_1324 -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324
v0)))
-- Relation.Binary.Lattice.BoundedLattice.boundedMeetSemilattice
d_boundedMeetSemilattice_1430 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedLattice_1324 -> T_BoundedMeetSemilattice_706
d_boundedMeetSemilattice_1430 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedLattice_1324
-> T_BoundedMeetSemilattice_706
d_boundedMeetSemilattice_1430 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedLattice_1324
v3
  = T_BoundedLattice_1324 -> T_BoundedMeetSemilattice_706
du_boundedMeetSemilattice_1430 T_BoundedLattice_1324
v3
du_boundedMeetSemilattice_1430 ::
  T_BoundedLattice_1324 -> T_BoundedMeetSemilattice_706
du_boundedMeetSemilattice_1430 :: T_BoundedLattice_1324 -> T_BoundedMeetSemilattice_706
du_boundedMeetSemilattice_1430 T_BoundedLattice_1324
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> T_IsBoundedMeetSemilattice_632
 -> T_BoundedMeetSemilattice_706)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_BoundedMeetSemilattice_706
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedMeetSemilattice_632
-> T_BoundedMeetSemilattice_706
C_BoundedMeetSemilattice'46'constructor_23291
      (T_BoundedLattice_1324 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__1356 (T_BoundedLattice_1324 -> T_BoundedLattice_1324
forall a b. a -> b
coe T_BoundedLattice_1324
v0)) (T_BoundedLattice_1324 -> AgdaAny
d_'8868'_1358 (T_BoundedLattice_1324 -> T_BoundedLattice_1324
forall a b. a -> b
coe T_BoundedLattice_1324
v0))
      ((T_IsBoundedLattice_1226 -> T_IsBoundedMeetSemilattice_632)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBoundedLattice_1226 -> T_IsBoundedMeetSemilattice_632
du_isBoundedMeetSemilattice_1316
         ((T_BoundedLattice_1324 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (T_BoundedLattice_1324 -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324
v0)))
-- Relation.Binary.Lattice.BoundedLattice.lattice
d_lattice_1432 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedLattice_1324 -> T_Lattice_898
d_lattice_1432 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedLattice_1324
-> T_Lattice_898
d_lattice_1432 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedLattice_1324
v3 = T_BoundedLattice_1324 -> T_Lattice_898
du_lattice_1432 T_BoundedLattice_1324
v3
du_lattice_1432 :: T_BoundedLattice_1324 -> T_Lattice_898
du_lattice_1432 :: T_BoundedLattice_1324 -> T_Lattice_898
du_lattice_1432 T_BoundedLattice_1324
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsLattice_810
 -> T_Lattice_898)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_810
-> T_Lattice_898
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_810
-> T_Lattice_898
C_Lattice'46'constructor_30305 (T_BoundedLattice_1324 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__1354 (T_BoundedLattice_1324 -> T_BoundedLattice_1324
forall a b. a -> b
coe T_BoundedLattice_1324
v0))
      (T_BoundedLattice_1324 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__1356 (T_BoundedLattice_1324 -> T_BoundedLattice_1324
forall a b. a -> b
coe T_BoundedLattice_1324
v0))
      (T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 ((T_BoundedLattice_1324 -> T_IsBoundedLattice_1226)
-> AgdaAny -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (T_BoundedLattice_1324 -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324
v0)))
-- Relation.Binary.Lattice.BoundedLattice._.joinSemilattice
d_joinSemilattice_1436 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedLattice_1324 -> T_JoinSemilattice_170
d_joinSemilattice_1436 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedLattice_1324
-> T_JoinSemilattice_170
d_joinSemilattice_1436 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedLattice_1324
v3 = T_BoundedLattice_1324 -> T_JoinSemilattice_170
du_joinSemilattice_1436 T_BoundedLattice_1324
v3
du_joinSemilattice_1436 ::
  T_BoundedLattice_1324 -> T_JoinSemilattice_170
du_joinSemilattice_1436 :: T_BoundedLattice_1324 -> T_JoinSemilattice_170
du_joinSemilattice_1436 T_BoundedLattice_1324
v0
  = (T_Lattice_898 -> T_JoinSemilattice_170)
-> AgdaAny -> T_JoinSemilattice_170
forall a b. a -> b
coe T_Lattice_898 -> T_JoinSemilattice_170
du_joinSemilattice_986 ((T_BoundedLattice_1324 -> T_Lattice_898) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324 -> T_Lattice_898
du_lattice_1432 (T_BoundedLattice_1324 -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324
v0))
-- Relation.Binary.Lattice.BoundedLattice._.meetSemilattice
d_meetSemilattice_1438 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedLattice_1324 -> T_MeetSemilattice_540
d_meetSemilattice_1438 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedLattice_1324
-> T_MeetSemilattice_540
d_meetSemilattice_1438 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedLattice_1324
v3 = T_BoundedLattice_1324 -> T_MeetSemilattice_540
du_meetSemilattice_1438 T_BoundedLattice_1324
v3
du_meetSemilattice_1438 ::
  T_BoundedLattice_1324 -> T_MeetSemilattice_540
du_meetSemilattice_1438 :: T_BoundedLattice_1324 -> T_MeetSemilattice_540
du_meetSemilattice_1438 T_BoundedLattice_1324
v0
  = (T_Lattice_898 -> T_MeetSemilattice_540)
-> AgdaAny -> T_MeetSemilattice_540
forall a b. a -> b
coe T_Lattice_898 -> T_MeetSemilattice_540
du_meetSemilattice_988 ((T_BoundedLattice_1324 -> T_Lattice_898) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324 -> T_Lattice_898
du_lattice_1432 (T_BoundedLattice_1324 -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324
v0))
-- Relation.Binary.Lattice.BoundedLattice._.poset
d_poset_1440 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedLattice_1324 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Poset_282
d_poset_1440 :: T_Level_18
-> T_Level_18 -> T_Level_18 -> T_BoundedLattice_1324 -> T_Poset_282
d_poset_1440 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedLattice_1324
v3 = T_BoundedLattice_1324 -> T_Poset_282
du_poset_1440 T_BoundedLattice_1324
v3
du_poset_1440 ::
  T_BoundedLattice_1324 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Poset_282
du_poset_1440 :: T_BoundedLattice_1324 -> T_Poset_282
du_poset_1440 T_BoundedLattice_1324
v0
  = let v1 :: t
v1 = (T_BoundedLattice_1324 -> T_Lattice_898) -> AgdaAny -> t
forall a b. a -> b
coe T_BoundedLattice_1324 -> T_Lattice_898
du_lattice_1432 (T_BoundedLattice_1324 -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324
v0) in
    AgdaAny -> T_Poset_282
forall a b. a -> b
coe ((T_JoinSemilattice_170 -> T_Poset_282) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_170 -> T_Poset_282
du_poset_240 ((T_Lattice_898 -> T_JoinSemilattice_170) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_898 -> T_JoinSemilattice_170
du_joinSemilattice_986 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Relation.Binary.Lattice.BoundedLattice._.preorder
d_preorder_1442 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedLattice_1324 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Preorder_132
d_preorder_1442 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BoundedLattice_1324
-> T_Preorder_132
d_preorder_1442 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedLattice_1324
v3 = T_BoundedLattice_1324 -> T_Preorder_132
du_preorder_1442 T_BoundedLattice_1324
v3
du_preorder_1442 ::
  T_BoundedLattice_1324 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Preorder_132
du_preorder_1442 :: T_BoundedLattice_1324 -> T_Preorder_132
du_preorder_1442 T_BoundedLattice_1324
v0
  = let v1 :: t
v1 = (T_BoundedLattice_1324 -> T_Lattice_898) -> AgdaAny -> t
forall a b. a -> b
coe T_BoundedLattice_1324 -> T_Lattice_898
du_lattice_1432 (T_BoundedLattice_1324 -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324
v0) in
    AgdaAny -> T_Preorder_132
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_Lattice_898 -> T_JoinSemilattice_170) -> AgdaAny -> t
forall a b. a -> b
coe T_Lattice_898 -> T_JoinSemilattice_170
du_joinSemilattice_986 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Poset_282 -> T_Preorder_132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Poset_282 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_326
            ((T_JoinSemilattice_170 -> T_Poset_282) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_170 -> T_Poset_282
du_poset_240 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Relation.Binary.Lattice.BoundedLattice._.setoid
d_setoid_1444 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BoundedLattice_1324 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1444 :: T_Level_18
-> T_Level_18 -> T_Level_18 -> T_BoundedLattice_1324 -> T_Setoid_44
d_setoid_1444 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BoundedLattice_1324
v3 = T_BoundedLattice_1324 -> T_Setoid_44
du_setoid_1444 T_BoundedLattice_1324
v3
du_setoid_1444 ::
  T_BoundedLattice_1324 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1444 :: T_BoundedLattice_1324 -> T_Setoid_44
du_setoid_1444 T_BoundedLattice_1324
v0
  = (T_Lattice_898 -> T_Setoid_44) -> AgdaAny -> T_Setoid_44
forall a b. a -> b
coe T_Lattice_898 -> T_Setoid_44
du_setoid_984 ((T_BoundedLattice_1324 -> T_Lattice_898) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324 -> T_Lattice_898
du_lattice_1432 (T_BoundedLattice_1324 -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324
v0))
-- Relation.Binary.Lattice.IsHeytingAlgebra
d_IsHeytingAlgebra_1468 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsHeytingAlgebra_1468 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 p
a9 p
a10 = ()
data T_IsHeytingAlgebra_1468
  = C_IsHeytingAlgebra'46'constructor_48411 T_IsBoundedLattice_1226
                                            (AgdaAny ->
                                             AgdaAny ->
                                             AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14)
-- Relation.Binary.Lattice.IsHeytingAlgebra.isBoundedLattice
d_isBoundedLattice_1496 ::
  T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 :: T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 T_IsHeytingAlgebra_1468
v0
  = case T_IsHeytingAlgebra_1468 -> T_IsHeytingAlgebra_1468
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v0 of
      C_IsHeytingAlgebra'46'constructor_48411 T_IsBoundedLattice_1226
v1 AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
v2 -> T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v1
      T_IsHeytingAlgebra_1468
_ -> T_IsBoundedLattice_1226
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.IsHeytingAlgebra.exponential
d_exponential_1498 ::
  T_IsHeytingAlgebra_1468 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_exponential_1498 :: T_IsHeytingAlgebra_1468 -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
d_exponential_1498 T_IsHeytingAlgebra_1468
v0
  = case T_IsHeytingAlgebra_1468 -> T_IsHeytingAlgebra_1468
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v0 of
      C_IsHeytingAlgebra'46'constructor_48411 T_IsBoundedLattice_1226
v1 AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
v2 -> (AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
v2
      T_IsHeytingAlgebra_1468
_ -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.IsHeytingAlgebra.transpose-⇨
d_transpose'45''8680'_1506 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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 -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsHeytingAlgebra_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_transpose'45''8680'_1506 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_1468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_transpose'45''8680'_1506 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny -> AgdaAny
v8 ~AgdaAny
v9
                           ~AgdaAny
v10 T_IsHeytingAlgebra_1468
v11 AgdaAny
v12 AgdaAny
v13 AgdaAny
v14
  = T_IsHeytingAlgebra_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8680'_1506 T_IsHeytingAlgebra_1468
v11 AgdaAny
v12 AgdaAny
v13 AgdaAny
v14
du_transpose'45''8680'_1506 ::
  T_IsHeytingAlgebra_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8680'_1506 :: T_IsHeytingAlgebra_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8680'_1506 T_IsHeytingAlgebra_1468
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3
  = (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_IsHeytingAlgebra_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14)
-> T_IsHeytingAlgebra_1468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_1468 -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
d_exponential_1498 T_IsHeytingAlgebra_1468
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3)
-- Relation.Binary.Lattice.IsHeytingAlgebra.transpose-∧
d_transpose'45''8743'_1522 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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 -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsHeytingAlgebra_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_transpose'45''8743'_1522 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_1468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_transpose'45''8743'_1522 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny -> AgdaAny
v8 ~AgdaAny
v9
                           ~AgdaAny
v10 T_IsHeytingAlgebra_1468
v11 AgdaAny
v12 AgdaAny
v13 AgdaAny
v14
  = T_IsHeytingAlgebra_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8743'_1522 T_IsHeytingAlgebra_1468
v11 AgdaAny
v12 AgdaAny
v13 AgdaAny
v14
du_transpose'45''8743'_1522 ::
  T_IsHeytingAlgebra_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8743'_1522 :: T_IsHeytingAlgebra_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8743'_1522 T_IsHeytingAlgebra_1468
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3
  = (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_IsHeytingAlgebra_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14)
-> T_IsHeytingAlgebra_1468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_1468 -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
d_exponential_1498 T_IsHeytingAlgebra_1468
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3)
-- Relation.Binary.Lattice.IsHeytingAlgebra._.antisym
d_antisym_1534 ::
  T_IsHeytingAlgebra_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_1534 :: T_IsHeytingAlgebra_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_1534 T_IsHeytingAlgebra_1468
v0
  = (T_IsPartialOrder_162
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_162
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_172
      ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
         ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v0))))
-- Relation.Binary.Lattice.IsHeytingAlgebra._.infimum
d_infimum_1536 ::
  T_IsHeytingAlgebra_1468 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_infimum_1536 :: T_IsHeytingAlgebra_1468 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_1536 T_IsHeytingAlgebra_1468
v0
  = (T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_838
      ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v0)))
-- Relation.Binary.Lattice.IsHeytingAlgebra._.isBoundedJoinSemilattice
d_isBoundedJoinSemilattice_1538 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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 -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsHeytingAlgebra_1468 -> T_IsBoundedJoinSemilattice_262
d_isBoundedJoinSemilattice_1538 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_1468
-> T_IsBoundedJoinSemilattice_262
d_isBoundedJoinSemilattice_1538 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny -> AgdaAny
v8
                                ~AgdaAny
v9 ~AgdaAny
v10 T_IsHeytingAlgebra_1468
v11
  = T_IsHeytingAlgebra_1468 -> T_IsBoundedJoinSemilattice_262
du_isBoundedJoinSemilattice_1538 T_IsHeytingAlgebra_1468
v11
du_isBoundedJoinSemilattice_1538 ::
  T_IsHeytingAlgebra_1468 -> T_IsBoundedJoinSemilattice_262
du_isBoundedJoinSemilattice_1538 :: T_IsHeytingAlgebra_1468 -> T_IsBoundedJoinSemilattice_262
du_isBoundedJoinSemilattice_1538 T_IsHeytingAlgebra_1468
v0
  = (T_IsBoundedLattice_1226 -> T_IsBoundedJoinSemilattice_262)
-> AgdaAny -> T_IsBoundedJoinSemilattice_262
forall a b. a -> b
coe
      T_IsBoundedLattice_1226 -> T_IsBoundedJoinSemilattice_262
du_isBoundedJoinSemilattice_1314
      ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v0))
-- Relation.Binary.Lattice.IsHeytingAlgebra._.isBoundedMeetSemilattice
d_isBoundedMeetSemilattice_1540 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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 -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsHeytingAlgebra_1468 -> T_IsBoundedMeetSemilattice_632
d_isBoundedMeetSemilattice_1540 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_1468
-> T_IsBoundedMeetSemilattice_632
d_isBoundedMeetSemilattice_1540 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny -> AgdaAny
v8
                                ~AgdaAny
v9 ~AgdaAny
v10 T_IsHeytingAlgebra_1468
v11
  = T_IsHeytingAlgebra_1468 -> T_IsBoundedMeetSemilattice_632
du_isBoundedMeetSemilattice_1540 T_IsHeytingAlgebra_1468
v11
du_isBoundedMeetSemilattice_1540 ::
  T_IsHeytingAlgebra_1468 -> T_IsBoundedMeetSemilattice_632
du_isBoundedMeetSemilattice_1540 :: T_IsHeytingAlgebra_1468 -> T_IsBoundedMeetSemilattice_632
du_isBoundedMeetSemilattice_1540 T_IsHeytingAlgebra_1468
v0
  = (T_IsBoundedLattice_1226 -> T_IsBoundedMeetSemilattice_632)
-> AgdaAny -> T_IsBoundedMeetSemilattice_632
forall a b. a -> b
coe
      T_IsBoundedLattice_1226 -> T_IsBoundedMeetSemilattice_632
du_isBoundedMeetSemilattice_1316
      ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v0))
-- Relation.Binary.Lattice.IsHeytingAlgebra._.isEquivalence
d_isEquivalence_1542 ::
  T_IsHeytingAlgebra_1468 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1542 :: T_IsHeytingAlgebra_1468 -> T_IsEquivalence_26
d_isEquivalence_1542 T_IsHeytingAlgebra_1468
v0
  = (T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
            ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v0)))))
-- Relation.Binary.Lattice.IsHeytingAlgebra._.isJoinSemilattice
d_isJoinSemilattice_1544 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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 -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsHeytingAlgebra_1468 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_1544 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_1468
-> T_IsJoinSemilattice_68
d_isJoinSemilattice_1544 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny -> AgdaAny
v8 ~AgdaAny
v9
                         ~AgdaAny
v10 T_IsHeytingAlgebra_1468
v11
  = T_IsHeytingAlgebra_1468 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_1544 T_IsHeytingAlgebra_1468
v11
du_isJoinSemilattice_1544 ::
  T_IsHeytingAlgebra_1468 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_1544 :: T_IsHeytingAlgebra_1468 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_1544 T_IsHeytingAlgebra_1468
v0
  = let v1 :: T_IsBoundedLattice_1226
v1 = T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> T_IsHeytingAlgebra_1468
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v0) in
    AgdaAny -> T_IsJoinSemilattice_68
forall a b. a -> b
coe ((T_IsLattice_810 -> T_IsJoinSemilattice_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226
v1)))
-- Relation.Binary.Lattice.IsHeytingAlgebra._.isLattice
d_isLattice_1546 :: T_IsHeytingAlgebra_1468 -> T_IsLattice_810
d_isLattice_1546 :: T_IsHeytingAlgebra_1468 -> T_IsLattice_810
d_isLattice_1546 T_IsHeytingAlgebra_1468
v0
  = (T_IsBoundedLattice_1226 -> T_IsLattice_810)
-> AgdaAny -> T_IsLattice_810
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v0))
-- Relation.Binary.Lattice.IsHeytingAlgebra._.isMeetSemilattice
d_isMeetSemilattice_1548 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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 -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsHeytingAlgebra_1468 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_1548 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_1468
-> T_IsMeetSemilattice_438
d_isMeetSemilattice_1548 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny -> AgdaAny
v8 ~AgdaAny
v9
                         ~AgdaAny
v10 T_IsHeytingAlgebra_1468
v11
  = T_IsHeytingAlgebra_1468 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_1548 T_IsHeytingAlgebra_1468
v11
du_isMeetSemilattice_1548 ::
  T_IsHeytingAlgebra_1468 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_1548 :: T_IsHeytingAlgebra_1468 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_1548 T_IsHeytingAlgebra_1468
v0
  = let v1 :: T_IsBoundedLattice_1226
v1 = T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> T_IsHeytingAlgebra_1468
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v0) in
    AgdaAny -> T_IsMeetSemilattice_438
forall a b. a -> b
coe ((T_IsLattice_810 -> T_IsMeetSemilattice_438) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226
v1)))
-- Relation.Binary.Lattice.IsHeytingAlgebra._.isPartialOrder
d_isPartialOrder_1550 ::
  T_IsHeytingAlgebra_1468 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_162
d_isPartialOrder_1550 :: T_IsHeytingAlgebra_1468 -> T_IsPartialOrder_162
d_isPartialOrder_1550 T_IsHeytingAlgebra_1468
v0
  = (T_IsLattice_810 -> T_IsPartialOrder_162)
-> AgdaAny -> T_IsPartialOrder_162
forall a b. a -> b
coe
      T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
      ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v0)))
-- Relation.Binary.Lattice.IsHeytingAlgebra._.isPreorder
d_isPreorder_1552 ::
  T_IsHeytingAlgebra_1468 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_1552 :: T_IsHeytingAlgebra_1468 -> T_IsPreorder_70
d_isPreorder_1552 T_IsHeytingAlgebra_1468
v0
  = (T_IsPartialOrder_162 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
      ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
         ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v0))))
-- Relation.Binary.Lattice.IsHeytingAlgebra._.maximum
d_maximum_1554 :: T_IsHeytingAlgebra_1468 -> AgdaAny -> AgdaAny
d_maximum_1554 :: T_IsHeytingAlgebra_1468 -> AgdaAny -> AgdaAny
d_maximum_1554 T_IsHeytingAlgebra_1468
v0
  = (T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny
d_maximum_1256 ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v0))
-- Relation.Binary.Lattice.IsHeytingAlgebra._.minimum
d_minimum_1556 :: T_IsHeytingAlgebra_1468 -> AgdaAny -> AgdaAny
d_minimum_1556 :: T_IsHeytingAlgebra_1468 -> AgdaAny -> AgdaAny
d_minimum_1556 T_IsHeytingAlgebra_1468
v0
  = (T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny
d_minimum_1258 ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v0))
-- Relation.Binary.Lattice.IsHeytingAlgebra._.refl
d_refl_1558 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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 -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsHeytingAlgebra_1468 -> AgdaAny -> AgdaAny
d_refl_1558 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_1468
-> AgdaAny
-> AgdaAny
d_refl_1558 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10 T_IsHeytingAlgebra_1468
v11
  = T_IsHeytingAlgebra_1468 -> AgdaAny -> AgdaAny
du_refl_1558 T_IsHeytingAlgebra_1468
v11
du_refl_1558 :: T_IsHeytingAlgebra_1468 -> AgdaAny -> AgdaAny
du_refl_1558 :: T_IsHeytingAlgebra_1468 -> AgdaAny -> AgdaAny
du_refl_1558 T_IsHeytingAlgebra_1468
v0
  = let v1 :: T_IsBoundedLattice_1226
v1 = T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> T_IsHeytingAlgebra_1468
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_810
v2 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsPreorder_70 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_70 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_98
               ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                  (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v3)))))
-- Relation.Binary.Lattice.IsHeytingAlgebra._.reflexive
d_reflexive_1560 ::
  T_IsHeytingAlgebra_1468 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_1560 :: T_IsHeytingAlgebra_1468 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_1560 T_IsHeytingAlgebra_1468
v0
  = (T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
            ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v0)))))
-- Relation.Binary.Lattice.IsHeytingAlgebra._.supremum
d_supremum_1562 ::
  T_IsHeytingAlgebra_1468 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_supremum_1562 :: T_IsHeytingAlgebra_1468 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_1562 T_IsHeytingAlgebra_1468
v0
  = (T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_836
      ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v0)))
-- Relation.Binary.Lattice.IsHeytingAlgebra._.trans
d_trans_1564 ::
  T_IsHeytingAlgebra_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1564 :: T_IsHeytingAlgebra_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1564 T_IsHeytingAlgebra_1468
v0
  = (T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
            ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v0)))))
-- Relation.Binary.Lattice.IsHeytingAlgebra._.x∧y≤x
d_x'8743'y'8804'x_1566 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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 -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsHeytingAlgebra_1468 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'x_1566 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_1468
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'x_1566 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10
                       T_IsHeytingAlgebra_1468
v11
  = T_IsHeytingAlgebra_1468 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_1566 T_IsHeytingAlgebra_1468
v11
du_x'8743'y'8804'x_1566 ::
  T_IsHeytingAlgebra_1468 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_1566 :: T_IsHeytingAlgebra_1468 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_1566 T_IsHeytingAlgebra_1468
v0
  = let v1 :: T_IsBoundedLattice_1226
v1 = T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> T_IsHeytingAlgebra_1468
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_810
v2 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_466 ((T_IsLattice_810 -> T_IsMeetSemilattice_438) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v2))))
-- Relation.Binary.Lattice.IsHeytingAlgebra._.x∧y≤y
d_x'8743'y'8804'y_1568 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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 -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsHeytingAlgebra_1468 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'y_1568 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_1468
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'y_1568 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10
                       T_IsHeytingAlgebra_1468
v11
  = T_IsHeytingAlgebra_1468 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_1568 T_IsHeytingAlgebra_1468
v11
du_x'8743'y'8804'y_1568 ::
  T_IsHeytingAlgebra_1468 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_1568 :: T_IsHeytingAlgebra_1468 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_1568 T_IsHeytingAlgebra_1468
v0
  = let v1 :: T_IsBoundedLattice_1226
v1 = T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> T_IsHeytingAlgebra_1468
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_810
v2 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_478 ((T_IsLattice_810 -> T_IsMeetSemilattice_438) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v2))))
-- Relation.Binary.Lattice.IsHeytingAlgebra._.x≤x∨y
d_x'8804'x'8744'y_1570 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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 -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsHeytingAlgebra_1468 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8804'x'8744'y_1570 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_1468
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8804'x'8744'y_1570 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10
                       T_IsHeytingAlgebra_1468
v11
  = T_IsHeytingAlgebra_1468 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_1570 T_IsHeytingAlgebra_1468
v11
du_x'8804'x'8744'y_1570 ::
  T_IsHeytingAlgebra_1468 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_1570 :: T_IsHeytingAlgebra_1468 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_1570 T_IsHeytingAlgebra_1468
v0
  = let v1 :: T_IsBoundedLattice_1226
v1 = T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> T_IsHeytingAlgebra_1468
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_810
v2 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_96 ((T_IsLattice_810 -> T_IsJoinSemilattice_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v2))))
-- Relation.Binary.Lattice.IsHeytingAlgebra._.y≤x∨y
d_y'8804'x'8744'y_1572 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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 -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsHeytingAlgebra_1468 -> AgdaAny -> AgdaAny -> AgdaAny
d_y'8804'x'8744'y_1572 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_1468
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_y'8804'x'8744'y_1572 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10
                       T_IsHeytingAlgebra_1468
v11
  = T_IsHeytingAlgebra_1468 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_1572 T_IsHeytingAlgebra_1468
v11
du_y'8804'x'8744'y_1572 ::
  T_IsHeytingAlgebra_1468 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_1572 :: T_IsHeytingAlgebra_1468 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_1572 T_IsHeytingAlgebra_1468
v0
  = let v1 :: T_IsBoundedLattice_1226
v1 = T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> T_IsHeytingAlgebra_1468
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_810
v2 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_108 ((T_IsLattice_810 -> T_IsJoinSemilattice_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v2))))
-- Relation.Binary.Lattice.IsHeytingAlgebra._.∧-greatest
d_'8743''45'greatest_1574 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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 -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsHeytingAlgebra_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'greatest_1574 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_1468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'greatest_1574 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny -> AgdaAny
v8 ~AgdaAny
v9
                          ~AgdaAny
v10 T_IsHeytingAlgebra_1468
v11
  = T_IsHeytingAlgebra_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_1574 T_IsHeytingAlgebra_1468
v11
du_'8743''45'greatest_1574 ::
  T_IsHeytingAlgebra_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_1574 :: T_IsHeytingAlgebra_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_1574 T_IsHeytingAlgebra_1468
v0
  = let v1 :: T_IsBoundedLattice_1226
v1 = T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> T_IsHeytingAlgebra_1468
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_810
v2 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMeetSemilattice_438
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMeetSemilattice_438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_492 ((T_IsLattice_810 -> T_IsMeetSemilattice_438) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v2))))
-- Relation.Binary.Lattice.IsHeytingAlgebra._.∨-least
d_'8744''45'least_1576 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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 -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsHeytingAlgebra_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'least_1576 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_1468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'least_1576 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10
                       T_IsHeytingAlgebra_1468
v11
  = T_IsHeytingAlgebra_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_1576 T_IsHeytingAlgebra_1468
v11
du_'8744''45'least_1576 ::
  T_IsHeytingAlgebra_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_1576 :: T_IsHeytingAlgebra_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_1576 T_IsHeytingAlgebra_1468
v0
  = let v1 :: T_IsBoundedLattice_1226
v1 = T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> T_IsHeytingAlgebra_1468
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_810
v2 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsJoinSemilattice_68
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsJoinSemilattice_68
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_122 ((T_IsLattice_810 -> T_IsJoinSemilattice_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v2))))
-- Relation.Binary.Lattice.IsHeytingAlgebra._.∼-resp-≈
d_'8764''45'resp'45''8776'_1578 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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 -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsHeytingAlgebra_1468 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_1578 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_1468
-> T_Σ_14
d_'8764''45'resp'45''8776'_1578 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny -> AgdaAny
v8
                                ~AgdaAny
v9 ~AgdaAny
v10 T_IsHeytingAlgebra_1468
v11
  = T_IsHeytingAlgebra_1468 -> T_Σ_14
du_'8764''45'resp'45''8776'_1578 T_IsHeytingAlgebra_1468
v11
du_'8764''45'resp'45''8776'_1578 ::
  T_IsHeytingAlgebra_1468 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_1578 :: T_IsHeytingAlgebra_1468 -> T_Σ_14
du_'8764''45'resp'45''8776'_1578 T_IsHeytingAlgebra_1468
v0
  = let v1 :: T_IsBoundedLattice_1226
v1 = T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> T_IsHeytingAlgebra_1468
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_810
v2 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsPreorder_70 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_70 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_112
               ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                  (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v3)))))
-- Relation.Binary.Lattice.IsHeytingAlgebra._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_1580 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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 -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsHeytingAlgebra_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_1580 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_1468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_1580 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6
                                     ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10 T_IsHeytingAlgebra_1468
v11
  = T_IsHeytingAlgebra_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_1580 T_IsHeytingAlgebra_1468
v11
du_'8764''45'resp'691''45''8776'_1580 ::
  T_IsHeytingAlgebra_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_1580 :: T_IsHeytingAlgebra_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_1580 T_IsHeytingAlgebra_1468
v0
  = let v1 :: T_IsBoundedLattice_1226
v1 = T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> T_IsHeytingAlgebra_1468
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_810
v2 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_106
               ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                  (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v3)))))
-- Relation.Binary.Lattice.IsHeytingAlgebra._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_1582 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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 -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsHeytingAlgebra_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_1582 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_1468
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_1582 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6
                                     ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10 T_IsHeytingAlgebra_1468
v11
  = T_IsHeytingAlgebra_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_1582 T_IsHeytingAlgebra_1468
v11
du_'8764''45'resp'737''45''8776'_1582 ::
  T_IsHeytingAlgebra_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_1582 :: T_IsHeytingAlgebra_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_1582 T_IsHeytingAlgebra_1468
v0
  = let v1 :: T_IsBoundedLattice_1226
v1 = T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> T_IsHeytingAlgebra_1468
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_810
v2 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_100
               ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                  (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v3)))))
-- Relation.Binary.Lattice.IsHeytingAlgebra._.Eq.isPartialEquivalence
d_isPartialEquivalence_1586 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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 -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsHeytingAlgebra_1468 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1586 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_1468
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1586 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny -> AgdaAny
v8 ~AgdaAny
v9
                            ~AgdaAny
v10 T_IsHeytingAlgebra_1468
v11
  = T_IsHeytingAlgebra_1468 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1586 T_IsHeytingAlgebra_1468
v11
du_isPartialEquivalence_1586 ::
  T_IsHeytingAlgebra_1468 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1586 :: T_IsHeytingAlgebra_1468 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1586 T_IsHeytingAlgebra_1468
v0
  = let v1 :: T_IsBoundedLattice_1226
v1 = T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> T_IsHeytingAlgebra_1468
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_810
v2 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreorder_70
v4
                   = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                       (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                     (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v4))))))
-- Relation.Binary.Lattice.IsHeytingAlgebra._.Eq.refl
d_refl_1588 :: T_IsHeytingAlgebra_1468 -> AgdaAny -> AgdaAny
d_refl_1588 :: T_IsHeytingAlgebra_1468 -> AgdaAny -> AgdaAny
d_refl_1588 T_IsHeytingAlgebra_1468
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
               ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v0))))))
-- Relation.Binary.Lattice.IsHeytingAlgebra._.Eq.reflexive
d_reflexive_1590 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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 -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsHeytingAlgebra_1468 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1590 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_1468
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1590 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10 T_IsHeytingAlgebra_1468
v11
  = T_IsHeytingAlgebra_1468
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1590 T_IsHeytingAlgebra_1468
v11
du_reflexive_1590 ::
  T_IsHeytingAlgebra_1468 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1590 :: T_IsHeytingAlgebra_1468
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1590 T_IsHeytingAlgebra_1468
v0
  = let v1 :: T_IsBoundedLattice_1226
v1 = T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> T_IsHeytingAlgebra_1468
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_810
v2 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_162
v3 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreorder_70
v4
                   = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                       (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                       (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v4))
                    AgdaAny
v5))))
-- Relation.Binary.Lattice.IsHeytingAlgebra._.Eq.sym
d_sym_1592 ::
  T_IsHeytingAlgebra_1468 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1592 :: T_IsHeytingAlgebra_1468 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1592 T_IsHeytingAlgebra_1468
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
               ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v0))))))
-- Relation.Binary.Lattice.IsHeytingAlgebra._.Eq.trans
d_trans_1594 ::
  T_IsHeytingAlgebra_1468 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1594 :: T_IsHeytingAlgebra_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1594 T_IsHeytingAlgebra_1468
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
               ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v0))))))
-- Relation.Binary.Lattice.HeytingAlgebra
d_HeytingAlgebra_1602 :: p -> p -> p -> T_Level_18
d_HeytingAlgebra_1602 p
a0 p
a1 p
a2 = ()
data T_HeytingAlgebra_1602
  = C_HeytingAlgebra'46'constructor_55523 (AgdaAny ->
                                           AgdaAny -> AgdaAny)
                                          (AgdaAny -> AgdaAny -> AgdaAny)
                                          (AgdaAny -> AgdaAny -> AgdaAny) AgdaAny AgdaAny
                                          T_IsHeytingAlgebra_1468
-- Relation.Binary.Lattice.HeytingAlgebra.Carrier
d_Carrier_1628 :: T_HeytingAlgebra_1602 -> ()
d_Carrier_1628 :: T_HeytingAlgebra_1602 -> T_Level_18
d_Carrier_1628 = T_HeytingAlgebra_1602 -> T_Level_18
forall a. a
erased
-- Relation.Binary.Lattice.HeytingAlgebra._≈_
d__'8776'__1630 ::
  T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1630 :: T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> T_Level_18
d__'8776'__1630 = T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> T_Level_18
forall a. a
erased
-- Relation.Binary.Lattice.HeytingAlgebra._≤_
d__'8804'__1632 ::
  T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> ()
d__'8804'__1632 :: T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> T_Level_18
d__'8804'__1632 = T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> T_Level_18
forall a. a
erased
-- Relation.Binary.Lattice.HeytingAlgebra._∨_
d__'8744'__1634 ::
  T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__1634 :: T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__1634 T_HeytingAlgebra_1602
v0
  = case T_HeytingAlgebra_1602 -> T_HeytingAlgebra_1602
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0 of
      C_HeytingAlgebra'46'constructor_55523 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 T_IsHeytingAlgebra_1468
v9 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_HeytingAlgebra_1602
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.HeytingAlgebra._∧_
d__'8743'__1636 ::
  T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__1636 :: T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__1636 T_HeytingAlgebra_1602
v0
  = case T_HeytingAlgebra_1602 -> T_HeytingAlgebra_1602
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0 of
      C_HeytingAlgebra'46'constructor_55523 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 T_IsHeytingAlgebra_1468
v9 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v5
      T_HeytingAlgebra_1602
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.HeytingAlgebra._⇨_
d__'8680'__1638 ::
  T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8680'__1638 :: T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8680'__1638 T_HeytingAlgebra_1602
v0
  = case T_HeytingAlgebra_1602 -> T_HeytingAlgebra_1602
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0 of
      C_HeytingAlgebra'46'constructor_55523 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 T_IsHeytingAlgebra_1468
v9 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v6
      T_HeytingAlgebra_1602
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.HeytingAlgebra.⊤
d_'8868'_1640 :: T_HeytingAlgebra_1602 -> AgdaAny
d_'8868'_1640 :: T_HeytingAlgebra_1602 -> AgdaAny
d_'8868'_1640 T_HeytingAlgebra_1602
v0
  = case T_HeytingAlgebra_1602 -> T_HeytingAlgebra_1602
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0 of
      C_HeytingAlgebra'46'constructor_55523 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 T_IsHeytingAlgebra_1468
v9 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v7
      T_HeytingAlgebra_1602
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.HeytingAlgebra.⊥
d_'8869'_1642 :: T_HeytingAlgebra_1602 -> AgdaAny
d_'8869'_1642 :: T_HeytingAlgebra_1602 -> AgdaAny
d_'8869'_1642 T_HeytingAlgebra_1602
v0
  = case T_HeytingAlgebra_1602 -> T_HeytingAlgebra_1602
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0 of
      C_HeytingAlgebra'46'constructor_55523 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 T_IsHeytingAlgebra_1468
v9 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v8
      T_HeytingAlgebra_1602
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.HeytingAlgebra.isHeytingAlgebra
d_isHeytingAlgebra_1644 ::
  T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1644 :: T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1644 T_HeytingAlgebra_1602
v0
  = case T_HeytingAlgebra_1602 -> T_HeytingAlgebra_1602
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0 of
      C_HeytingAlgebra'46'constructor_55523 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 T_IsHeytingAlgebra_1468
v9 -> T_IsHeytingAlgebra_1468 -> T_IsHeytingAlgebra_1468
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v9
      T_HeytingAlgebra_1602
_ -> T_IsHeytingAlgebra_1468
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.HeytingAlgebra.boundedLattice
d_boundedLattice_1646 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
d_boundedLattice_1646 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_HeytingAlgebra_1602
-> T_BoundedLattice_1324
d_boundedLattice_1646 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3 = T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 T_HeytingAlgebra_1602
v3
du_boundedLattice_1646 ::
  T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 :: T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 T_HeytingAlgebra_1602
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> T_IsBoundedLattice_1226
 -> T_BoundedLattice_1324)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_1226
-> T_BoundedLattice_1324
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_1226
-> T_BoundedLattice_1324
C_BoundedLattice'46'constructor_44603 (T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__1634 (T_HeytingAlgebra_1602 -> T_HeytingAlgebra_1602
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0))
      (T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__1636 (T_HeytingAlgebra_1602 -> T_HeytingAlgebra_1602
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0)) (T_HeytingAlgebra_1602 -> AgdaAny
d_'8868'_1640 (T_HeytingAlgebra_1602 -> T_HeytingAlgebra_1602
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0))
      (T_HeytingAlgebra_1602 -> AgdaAny
d_'8869'_1642 (T_HeytingAlgebra_1602 -> T_HeytingAlgebra_1602
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0))
      (T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> T_IsHeytingAlgebra_1468
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1644 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0)))
-- Relation.Binary.Lattice.HeytingAlgebra._.exponential
d_exponential_1650 ::
  T_HeytingAlgebra_1602 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_exponential_1650 :: T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
d_exponential_1650 T_HeytingAlgebra_1602
v0
  = (T_IsHeytingAlgebra_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsHeytingAlgebra_1468 -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
d_exponential_1498 ((T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1644 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0))
-- Relation.Binary.Lattice.HeytingAlgebra._.transpose-⇨
d_transpose'45''8680'_1652 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_transpose'45''8680'_1652 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_HeytingAlgebra_1602
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_transpose'45''8680'_1652 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3
  = T_HeytingAlgebra_1602
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8680'_1652 T_HeytingAlgebra_1602
v3
du_transpose'45''8680'_1652 ::
  T_HeytingAlgebra_1602 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8680'_1652 :: T_HeytingAlgebra_1602
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8680'_1652 T_HeytingAlgebra_1602
v0
  = (T_IsHeytingAlgebra_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsHeytingAlgebra_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8680'_1506 ((T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1644 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0))
-- Relation.Binary.Lattice.HeytingAlgebra._.transpose-∧
d_transpose'45''8743'_1654 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_transpose'45''8743'_1654 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_HeytingAlgebra_1602
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_transpose'45''8743'_1654 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3
  = T_HeytingAlgebra_1602
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8743'_1654 T_HeytingAlgebra_1602
v3
du_transpose'45''8743'_1654 ::
  T_HeytingAlgebra_1602 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8743'_1654 :: T_HeytingAlgebra_1602
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8743'_1654 T_HeytingAlgebra_1602
v0
  = (T_IsHeytingAlgebra_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsHeytingAlgebra_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8743'_1522 ((T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1644 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0))
-- Relation.Binary.Lattice.HeytingAlgebra._.antisym
d_antisym_1658 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_1658 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_HeytingAlgebra_1602
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_antisym_1658 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3 = T_HeytingAlgebra_1602
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_antisym_1658 T_HeytingAlgebra_1602
v3
du_antisym_1658 ::
  T_HeytingAlgebra_1602 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_antisym_1658 :: T_HeytingAlgebra_1602
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_antisym_1658 T_HeytingAlgebra_1602
v0
  = (T_IsPartialOrder_162
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_162
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_172
      ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
         ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254
            ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1644 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0)))))
-- Relation.Binary.Lattice.HeytingAlgebra._.boundedJoinSemilattice
d_boundedJoinSemilattice_1660 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 -> T_BoundedJoinSemilattice_336
d_boundedJoinSemilattice_1660 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_HeytingAlgebra_1602
-> T_BoundedJoinSemilattice_336
d_boundedJoinSemilattice_1660 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3
  = T_HeytingAlgebra_1602 -> T_BoundedJoinSemilattice_336
du_boundedJoinSemilattice_1660 T_HeytingAlgebra_1602
v3
du_boundedJoinSemilattice_1660 ::
  T_HeytingAlgebra_1602 -> T_BoundedJoinSemilattice_336
du_boundedJoinSemilattice_1660 :: T_HeytingAlgebra_1602 -> T_BoundedJoinSemilattice_336
du_boundedJoinSemilattice_1660 T_HeytingAlgebra_1602
v0
  = (T_BoundedLattice_1324 -> T_BoundedJoinSemilattice_336)
-> AgdaAny -> T_BoundedJoinSemilattice_336
forall a b. a -> b
coe
      T_BoundedLattice_1324 -> T_BoundedJoinSemilattice_336
du_boundedJoinSemilattice_1428
      ((T_HeytingAlgebra_1602 -> T_BoundedLattice_1324)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0))
-- Relation.Binary.Lattice.HeytingAlgebra._.boundedMeetSemilattice
d_boundedMeetSemilattice_1662 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 -> T_BoundedMeetSemilattice_706
d_boundedMeetSemilattice_1662 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_HeytingAlgebra_1602
-> T_BoundedMeetSemilattice_706
d_boundedMeetSemilattice_1662 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3
  = T_HeytingAlgebra_1602 -> T_BoundedMeetSemilattice_706
du_boundedMeetSemilattice_1662 T_HeytingAlgebra_1602
v3
du_boundedMeetSemilattice_1662 ::
  T_HeytingAlgebra_1602 -> T_BoundedMeetSemilattice_706
du_boundedMeetSemilattice_1662 :: T_HeytingAlgebra_1602 -> T_BoundedMeetSemilattice_706
du_boundedMeetSemilattice_1662 T_HeytingAlgebra_1602
v0
  = (T_BoundedLattice_1324 -> T_BoundedMeetSemilattice_706)
-> AgdaAny -> T_BoundedMeetSemilattice_706
forall a b. a -> b
coe
      T_BoundedLattice_1324 -> T_BoundedMeetSemilattice_706
du_boundedMeetSemilattice_1430
      ((T_HeytingAlgebra_1602 -> T_BoundedLattice_1324)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0))
-- Relation.Binary.Lattice.HeytingAlgebra._.infimum
d_infimum_1664 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_infimum_1664 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_HeytingAlgebra_1602
-> AgdaAny
-> AgdaAny
-> T_Σ_14
d_infimum_1664 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3 = T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> T_Σ_14
du_infimum_1664 T_HeytingAlgebra_1602
v3
du_infimum_1664 ::
  T_HeytingAlgebra_1602 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_infimum_1664 :: T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> T_Σ_14
du_infimum_1664 T_HeytingAlgebra_1602
v0
  = (T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_838
      ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254
         ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1644 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0))))
-- Relation.Binary.Lattice.HeytingAlgebra._.isBoundedJoinSemilattice
d_isBoundedJoinSemilattice_1666 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 -> T_IsBoundedJoinSemilattice_262
d_isBoundedJoinSemilattice_1666 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_HeytingAlgebra_1602
-> T_IsBoundedJoinSemilattice_262
d_isBoundedJoinSemilattice_1666 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3
  = T_HeytingAlgebra_1602 -> T_IsBoundedJoinSemilattice_262
du_isBoundedJoinSemilattice_1666 T_HeytingAlgebra_1602
v3
du_isBoundedJoinSemilattice_1666 ::
  T_HeytingAlgebra_1602 -> T_IsBoundedJoinSemilattice_262
du_isBoundedJoinSemilattice_1666 :: T_HeytingAlgebra_1602 -> T_IsBoundedJoinSemilattice_262
du_isBoundedJoinSemilattice_1666 T_HeytingAlgebra_1602
v0
  = let v1 :: t
v1 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0) in
    AgdaAny -> T_IsBoundedJoinSemilattice_262
forall a b. a -> b
coe
      ((T_IsBoundedLattice_1226 -> T_IsBoundedJoinSemilattice_262)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBoundedLattice_1226 -> T_IsBoundedJoinSemilattice_262
du_isBoundedJoinSemilattice_1314
         ((T_BoundedLattice_1324 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Relation.Binary.Lattice.HeytingAlgebra._.isBoundedLattice
d_isBoundedLattice_1668 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1668 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_HeytingAlgebra_1602
-> T_IsBoundedLattice_1226
d_isBoundedLattice_1668 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3
  = T_HeytingAlgebra_1602 -> T_IsBoundedLattice_1226
du_isBoundedLattice_1668 T_HeytingAlgebra_1602
v3
du_isBoundedLattice_1668 ::
  T_HeytingAlgebra_1602 -> T_IsBoundedLattice_1226
du_isBoundedLattice_1668 :: T_HeytingAlgebra_1602 -> T_IsBoundedLattice_1226
du_isBoundedLattice_1668 T_HeytingAlgebra_1602
v0
  = (T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> T_IsBoundedLattice_1226
forall a b. a -> b
coe
      T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1644 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0))
-- Relation.Binary.Lattice.HeytingAlgebra._.isBoundedMeetSemilattice
d_isBoundedMeetSemilattice_1670 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 -> T_IsBoundedMeetSemilattice_632
d_isBoundedMeetSemilattice_1670 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_HeytingAlgebra_1602
-> T_IsBoundedMeetSemilattice_632
d_isBoundedMeetSemilattice_1670 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3
  = T_HeytingAlgebra_1602 -> T_IsBoundedMeetSemilattice_632
du_isBoundedMeetSemilattice_1670 T_HeytingAlgebra_1602
v3
du_isBoundedMeetSemilattice_1670 ::
  T_HeytingAlgebra_1602 -> T_IsBoundedMeetSemilattice_632
du_isBoundedMeetSemilattice_1670 :: T_HeytingAlgebra_1602 -> T_IsBoundedMeetSemilattice_632
du_isBoundedMeetSemilattice_1670 T_HeytingAlgebra_1602
v0
  = let v1 :: t
v1 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0) in
    AgdaAny -> T_IsBoundedMeetSemilattice_632
forall a b. a -> b
coe
      ((T_IsBoundedLattice_1226 -> T_IsBoundedMeetSemilattice_632)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBoundedLattice_1226 -> T_IsBoundedMeetSemilattice_632
du_isBoundedMeetSemilattice_1316
         ((T_BoundedLattice_1324 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Relation.Binary.Lattice.HeytingAlgebra._.isEquivalence
d_isEquivalence_1672 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1672 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_HeytingAlgebra_1602
-> T_IsEquivalence_26
d_isEquivalence_1672 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3 = T_HeytingAlgebra_1602 -> T_IsEquivalence_26
du_isEquivalence_1672 T_HeytingAlgebra_1602
v3
du_isEquivalence_1672 ::
  T_HeytingAlgebra_1602 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_1672 :: T_HeytingAlgebra_1602 -> T_IsEquivalence_26
du_isEquivalence_1672 T_HeytingAlgebra_1602
v0
  = (T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
            ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254
               ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1644 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0))))))
-- Relation.Binary.Lattice.HeytingAlgebra._.isJoinSemilattice
d_isJoinSemilattice_1674 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_1674 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_HeytingAlgebra_1602
-> T_IsJoinSemilattice_68
d_isJoinSemilattice_1674 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3
  = T_HeytingAlgebra_1602 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_1674 T_HeytingAlgebra_1602
v3
du_isJoinSemilattice_1674 ::
  T_HeytingAlgebra_1602 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_1674 :: T_HeytingAlgebra_1602 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_1674 T_HeytingAlgebra_1602
v0
  = let v1 :: t
v1 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0) in
    AgdaAny -> T_IsJoinSemilattice_68
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_1226
v2 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (AgdaAny -> T_BoundedLattice_1324
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsLattice_810 -> T_IsJoinSemilattice_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226
v2))))
-- Relation.Binary.Lattice.HeytingAlgebra._.isLattice
d_isLattice_1676 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 -> T_IsLattice_810
d_isLattice_1676 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_HeytingAlgebra_1602
-> T_IsLattice_810
d_isLattice_1676 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3 = T_HeytingAlgebra_1602 -> T_IsLattice_810
du_isLattice_1676 T_HeytingAlgebra_1602
v3
du_isLattice_1676 :: T_HeytingAlgebra_1602 -> T_IsLattice_810
du_isLattice_1676 :: T_HeytingAlgebra_1602 -> T_IsLattice_810
du_isLattice_1676 T_HeytingAlgebra_1602
v0
  = (T_IsBoundedLattice_1226 -> T_IsLattice_810)
-> AgdaAny -> T_IsLattice_810
forall a b. a -> b
coe
      T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254
      ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1644 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0)))
-- Relation.Binary.Lattice.HeytingAlgebra._.isMeetSemilattice
d_isMeetSemilattice_1678 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_1678 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_HeytingAlgebra_1602
-> T_IsMeetSemilattice_438
d_isMeetSemilattice_1678 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3
  = T_HeytingAlgebra_1602 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_1678 T_HeytingAlgebra_1602
v3
du_isMeetSemilattice_1678 ::
  T_HeytingAlgebra_1602 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_1678 :: T_HeytingAlgebra_1602 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_1678 T_HeytingAlgebra_1602
v0
  = let v1 :: t
v1 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0) in
    AgdaAny -> T_IsMeetSemilattice_438
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_1226
v2 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (AgdaAny -> T_BoundedLattice_1324
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsLattice_810 -> T_IsMeetSemilattice_438) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226
v2))))
-- Relation.Binary.Lattice.HeytingAlgebra._.isPartialOrder
d_isPartialOrder_1680 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_162
d_isPartialOrder_1680 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_HeytingAlgebra_1602
-> T_IsPartialOrder_162
d_isPartialOrder_1680 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3 = T_HeytingAlgebra_1602 -> T_IsPartialOrder_162
du_isPartialOrder_1680 T_HeytingAlgebra_1602
v3
du_isPartialOrder_1680 ::
  T_HeytingAlgebra_1602 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_162
du_isPartialOrder_1680 :: T_HeytingAlgebra_1602 -> T_IsPartialOrder_162
du_isPartialOrder_1680 T_HeytingAlgebra_1602
v0
  = (T_IsLattice_810 -> T_IsPartialOrder_162)
-> AgdaAny -> T_IsPartialOrder_162
forall a b. a -> b
coe
      T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
      ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254
         ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1644 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0))))
-- Relation.Binary.Lattice.HeytingAlgebra._.isPreorder
d_isPreorder_1682 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_1682 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_HeytingAlgebra_1602
-> T_IsPreorder_70
d_isPreorder_1682 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3 = T_HeytingAlgebra_1602 -> T_IsPreorder_70
du_isPreorder_1682 T_HeytingAlgebra_1602
v3
du_isPreorder_1682 ::
  T_HeytingAlgebra_1602 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
du_isPreorder_1682 :: T_HeytingAlgebra_1602 -> T_IsPreorder_70
du_isPreorder_1682 T_HeytingAlgebra_1602
v0
  = (T_IsPartialOrder_162 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
      ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
         ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254
            ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1644 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0)))))
-- Relation.Binary.Lattice.HeytingAlgebra._.joinSemilattice
d_joinSemilattice_1684 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 -> T_JoinSemilattice_170
d_joinSemilattice_1684 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_HeytingAlgebra_1602
-> T_JoinSemilattice_170
d_joinSemilattice_1684 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3 = T_HeytingAlgebra_1602 -> T_JoinSemilattice_170
du_joinSemilattice_1684 T_HeytingAlgebra_1602
v3
du_joinSemilattice_1684 ::
  T_HeytingAlgebra_1602 -> T_JoinSemilattice_170
du_joinSemilattice_1684 :: T_HeytingAlgebra_1602 -> T_JoinSemilattice_170
du_joinSemilattice_1684 T_HeytingAlgebra_1602
v0
  = let v1 :: t
v1 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0) in
    AgdaAny -> T_JoinSemilattice_170
forall a b. a -> b
coe ((T_Lattice_898 -> T_JoinSemilattice_170) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_898 -> T_JoinSemilattice_170
du_joinSemilattice_986 ((T_BoundedLattice_1324 -> T_Lattice_898) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324 -> T_Lattice_898
du_lattice_1432 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Relation.Binary.Lattice.HeytingAlgebra._.lattice
d_lattice_1686 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 -> T_Lattice_898
d_lattice_1686 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_HeytingAlgebra_1602
-> T_Lattice_898
d_lattice_1686 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3 = T_HeytingAlgebra_1602 -> T_Lattice_898
du_lattice_1686 T_HeytingAlgebra_1602
v3
du_lattice_1686 :: T_HeytingAlgebra_1602 -> T_Lattice_898
du_lattice_1686 :: T_HeytingAlgebra_1602 -> T_Lattice_898
du_lattice_1686 T_HeytingAlgebra_1602
v0
  = (T_BoundedLattice_1324 -> T_Lattice_898)
-> AgdaAny -> T_Lattice_898
forall a b. a -> b
coe T_BoundedLattice_1324 -> T_Lattice_898
du_lattice_1432 ((T_HeytingAlgebra_1602 -> T_BoundedLattice_1324)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0))
-- Relation.Binary.Lattice.HeytingAlgebra._.maximum
d_maximum_1688 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny
d_maximum_1688 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_HeytingAlgebra_1602
-> AgdaAny
-> AgdaAny
d_maximum_1688 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3 = T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny
du_maximum_1688 T_HeytingAlgebra_1602
v3
du_maximum_1688 :: T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny
du_maximum_1688 :: T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny
du_maximum_1688 T_HeytingAlgebra_1602
v0
  = (T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny
d_maximum_1256
      ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1644 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0)))
-- Relation.Binary.Lattice.HeytingAlgebra._.meetSemilattice
d_meetSemilattice_1690 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 -> T_MeetSemilattice_540
d_meetSemilattice_1690 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_HeytingAlgebra_1602
-> T_MeetSemilattice_540
d_meetSemilattice_1690 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3 = T_HeytingAlgebra_1602 -> T_MeetSemilattice_540
du_meetSemilattice_1690 T_HeytingAlgebra_1602
v3
du_meetSemilattice_1690 ::
  T_HeytingAlgebra_1602 -> T_MeetSemilattice_540
du_meetSemilattice_1690 :: T_HeytingAlgebra_1602 -> T_MeetSemilattice_540
du_meetSemilattice_1690 T_HeytingAlgebra_1602
v0
  = let v1 :: t
v1 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0) in
    AgdaAny -> T_MeetSemilattice_540
forall a b. a -> b
coe ((T_Lattice_898 -> T_MeetSemilattice_540) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_898 -> T_MeetSemilattice_540
du_meetSemilattice_988 ((T_BoundedLattice_1324 -> T_Lattice_898) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324 -> T_Lattice_898
du_lattice_1432 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Relation.Binary.Lattice.HeytingAlgebra._.minimum
d_minimum_1692 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny
d_minimum_1692 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_HeytingAlgebra_1602
-> AgdaAny
-> AgdaAny
d_minimum_1692 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3 = T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny
du_minimum_1692 T_HeytingAlgebra_1602
v3
du_minimum_1692 :: T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny
du_minimum_1692 :: T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny
du_minimum_1692 T_HeytingAlgebra_1602
v0
  = (T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny
d_minimum_1258
      ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1644 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0)))
-- Relation.Binary.Lattice.HeytingAlgebra._.poset
d_poset_1694 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Poset_282
d_poset_1694 :: T_Level_18
-> T_Level_18 -> T_Level_18 -> T_HeytingAlgebra_1602 -> T_Poset_282
d_poset_1694 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3 = T_HeytingAlgebra_1602 -> T_Poset_282
du_poset_1694 T_HeytingAlgebra_1602
v3
du_poset_1694 ::
  T_HeytingAlgebra_1602 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Poset_282
du_poset_1694 :: T_HeytingAlgebra_1602 -> T_Poset_282
du_poset_1694 T_HeytingAlgebra_1602
v0
  = let v1 :: t
v1 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0) in
    AgdaAny -> T_Poset_282
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_BoundedLattice_1324 -> T_Lattice_898) -> AgdaAny -> t
forall a b. a -> b
coe T_BoundedLattice_1324 -> T_Lattice_898
du_lattice_1432 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_JoinSemilattice_170 -> T_Poset_282) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_170 -> T_Poset_282
du_poset_240 ((T_Lattice_898 -> T_JoinSemilattice_170) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_898 -> T_JoinSemilattice_170
du_joinSemilattice_986 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Relation.Binary.Lattice.HeytingAlgebra._.preorder
d_preorder_1696 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Preorder_132
d_preorder_1696 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_HeytingAlgebra_1602
-> T_Preorder_132
d_preorder_1696 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3 = T_HeytingAlgebra_1602 -> T_Preorder_132
du_preorder_1696 T_HeytingAlgebra_1602
v3
du_preorder_1696 ::
  T_HeytingAlgebra_1602 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Preorder_132
du_preorder_1696 :: T_HeytingAlgebra_1602 -> T_Preorder_132
du_preorder_1696 T_HeytingAlgebra_1602
v0
  = let v1 :: t
v1 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0) in
    AgdaAny -> T_Preorder_132
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_BoundedLattice_1324 -> T_Lattice_898) -> AgdaAny -> t
forall a b. a -> b
coe T_BoundedLattice_1324 -> T_Lattice_898
du_lattice_1432 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_Lattice_898 -> T_JoinSemilattice_170) -> AgdaAny -> t
forall a b. a -> b
coe T_Lattice_898 -> T_JoinSemilattice_170
du_joinSemilattice_986 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_Poset_282 -> T_Preorder_132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Poset_282 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_326
               ((T_JoinSemilattice_170 -> T_Poset_282) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_170 -> T_Poset_282
du_poset_240 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Relation.Binary.Lattice.HeytingAlgebra._.refl
d_refl_1698 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny
d_refl_1698 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_HeytingAlgebra_1602
-> AgdaAny
-> AgdaAny
d_refl_1698 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3 = T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny
du_refl_1698 T_HeytingAlgebra_1602
v3
du_refl_1698 :: T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny
du_refl_1698 :: T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny
du_refl_1698 T_HeytingAlgebra_1602
v0
  = let v1 :: t
v1 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_1226
v2 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (AgdaAny -> T_BoundedLattice_1324
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_810
v3 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_162
v4 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsPreorder_70 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_70 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_98
                  ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                     (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v4))))))
-- Relation.Binary.Lattice.HeytingAlgebra._.reflexive
d_reflexive_1700 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_1700 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_HeytingAlgebra_1602
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_reflexive_1700 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3 = T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_reflexive_1700 T_HeytingAlgebra_1602
v3
du_reflexive_1700 ::
  T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_reflexive_1700 :: T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_reflexive_1700 T_HeytingAlgebra_1602
v0
  = (T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
            ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254
               ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1644 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0))))))
-- Relation.Binary.Lattice.HeytingAlgebra._.setoid
d_setoid_1702 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1702 :: T_Level_18
-> T_Level_18 -> T_Level_18 -> T_HeytingAlgebra_1602 -> T_Setoid_44
d_setoid_1702 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3 = T_HeytingAlgebra_1602 -> T_Setoid_44
du_setoid_1702 T_HeytingAlgebra_1602
v3
du_setoid_1702 ::
  T_HeytingAlgebra_1602 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1702 :: T_HeytingAlgebra_1602 -> T_Setoid_44
du_setoid_1702 T_HeytingAlgebra_1602
v0
  = let v1 :: t
v1 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe ((T_Lattice_898 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_898 -> T_Setoid_44
du_setoid_984 ((T_BoundedLattice_1324 -> T_Lattice_898) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324 -> T_Lattice_898
du_lattice_1432 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Relation.Binary.Lattice.HeytingAlgebra._.supremum
d_supremum_1704 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_supremum_1704 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_HeytingAlgebra_1602
-> AgdaAny
-> AgdaAny
-> T_Σ_14
d_supremum_1704 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3 = T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> T_Σ_14
du_supremum_1704 T_HeytingAlgebra_1602
v3
du_supremum_1704 ::
  T_HeytingAlgebra_1602 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_supremum_1704 :: T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> T_Σ_14
du_supremum_1704 T_HeytingAlgebra_1602
v0
  = (T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_836
      ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254
         ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1644 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0))))
-- Relation.Binary.Lattice.HeytingAlgebra._.trans
d_trans_1706 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1706 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_HeytingAlgebra_1602
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_1706 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3 = T_HeytingAlgebra_1602
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1706 T_HeytingAlgebra_1602
v3
du_trans_1706 ::
  T_HeytingAlgebra_1602 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1706 :: T_HeytingAlgebra_1602
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1706 T_HeytingAlgebra_1602
v0
  = (T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
            ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254
               ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1644 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0))))))
-- Relation.Binary.Lattice.HeytingAlgebra._.x∧y≤x
d_x'8743'y'8804'x_1708 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'x_1708 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_HeytingAlgebra_1602
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'x_1708 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3 = T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_1708 T_HeytingAlgebra_1602
v3
du_x'8743'y'8804'x_1708 ::
  T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_1708 :: T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_1708 T_HeytingAlgebra_1602
v0
  = let v1 :: t
v1 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_1226
v2 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (AgdaAny -> T_BoundedLattice_1324
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_810
v3 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_466 ((T_IsLattice_810 -> T_IsMeetSemilattice_438) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v3)))))
-- Relation.Binary.Lattice.HeytingAlgebra._.x∧y≤y
d_x'8743'y'8804'y_1710 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'y_1710 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_HeytingAlgebra_1602
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'y_1710 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3 = T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_1710 T_HeytingAlgebra_1602
v3
du_x'8743'y'8804'y_1710 ::
  T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_1710 :: T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_1710 T_HeytingAlgebra_1602
v0
  = let v1 :: t
v1 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_1226
v2 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (AgdaAny -> T_BoundedLattice_1324
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_810
v3 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_478 ((T_IsLattice_810 -> T_IsMeetSemilattice_438) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v3)))))
-- Relation.Binary.Lattice.HeytingAlgebra._.x≤x∨y
d_x'8804'x'8744'y_1712 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8804'x'8744'y_1712 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_HeytingAlgebra_1602
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8804'x'8744'y_1712 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3 = T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_1712 T_HeytingAlgebra_1602
v3
du_x'8804'x'8744'y_1712 ::
  T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_1712 :: T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_1712 T_HeytingAlgebra_1602
v0
  = let v1 :: t
v1 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_1226
v2 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (AgdaAny -> T_BoundedLattice_1324
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_810
v3 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_96 ((T_IsLattice_810 -> T_IsJoinSemilattice_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v3)))))
-- Relation.Binary.Lattice.HeytingAlgebra._.y≤x∨y
d_y'8804'x'8744'y_1714 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> AgdaAny
d_y'8804'x'8744'y_1714 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_HeytingAlgebra_1602
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_y'8804'x'8744'y_1714 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3 = T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_1714 T_HeytingAlgebra_1602
v3
du_y'8804'x'8744'y_1714 ::
  T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_1714 :: T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_1714 T_HeytingAlgebra_1602
v0
  = let v1 :: t
v1 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_1226
v2 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (AgdaAny -> T_BoundedLattice_1324
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_810
v3 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_108 ((T_IsLattice_810 -> T_IsJoinSemilattice_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v3)))))
-- Relation.Binary.Lattice.HeytingAlgebra._.∧-greatest
d_'8743''45'greatest_1716 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'greatest_1716 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_HeytingAlgebra_1602
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'greatest_1716 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3
  = T_HeytingAlgebra_1602
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_1716 T_HeytingAlgebra_1602
v3
du_'8743''45'greatest_1716 ::
  T_HeytingAlgebra_1602 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_1716 :: T_HeytingAlgebra_1602
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_1716 T_HeytingAlgebra_1602
v0
  = let v1 :: t
v1 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_1226
v2 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (AgdaAny -> T_BoundedLattice_1324
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_810
v3 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMeetSemilattice_438
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMeetSemilattice_438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_492
               ((T_IsLattice_810 -> T_IsMeetSemilattice_438) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v3)))))
-- Relation.Binary.Lattice.HeytingAlgebra._.∨-least
d_'8744''45'least_1718 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'least_1718 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_HeytingAlgebra_1602
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'least_1718 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3 = T_HeytingAlgebra_1602
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_1718 T_HeytingAlgebra_1602
v3
du_'8744''45'least_1718 ::
  T_HeytingAlgebra_1602 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_1718 :: T_HeytingAlgebra_1602
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_1718 T_HeytingAlgebra_1602
v0
  = let v1 :: t
v1 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_1226
v2 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (AgdaAny -> T_BoundedLattice_1324
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_810
v3 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsJoinSemilattice_68
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsJoinSemilattice_68
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_122 ((T_IsLattice_810 -> T_IsJoinSemilattice_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v3)))))
-- Relation.Binary.Lattice.HeytingAlgebra._.∼-resp-≈
d_'8764''45'resp'45''8776'_1720 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_1720 :: T_Level_18
-> T_Level_18 -> T_Level_18 -> T_HeytingAlgebra_1602 -> T_Σ_14
d_'8764''45'resp'45''8776'_1720 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3
  = T_HeytingAlgebra_1602 -> T_Σ_14
du_'8764''45'resp'45''8776'_1720 T_HeytingAlgebra_1602
v3
du_'8764''45'resp'45''8776'_1720 ::
  T_HeytingAlgebra_1602 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_1720 :: T_HeytingAlgebra_1602 -> T_Σ_14
du_'8764''45'resp'45''8776'_1720 T_HeytingAlgebra_1602
v0
  = let v1 :: t
v1 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_1226
v2 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (AgdaAny -> T_BoundedLattice_1324
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_810
v3 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_162
v4 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsPreorder_70 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_70 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_112
                  ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                     (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v4))))))
-- Relation.Binary.Lattice.HeytingAlgebra._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_1722 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_1722 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_HeytingAlgebra_1602
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_1722 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3
  = T_HeytingAlgebra_1602
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_1722 T_HeytingAlgebra_1602
v3
du_'8764''45'resp'691''45''8776'_1722 ::
  T_HeytingAlgebra_1602 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_1722 :: T_HeytingAlgebra_1602
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_1722 T_HeytingAlgebra_1602
v0
  = let v1 :: t
v1 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_1226
v2 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (AgdaAny -> T_BoundedLattice_1324
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_810
v3 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_162
v4 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_106
                  ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                     (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v4))))))
-- Relation.Binary.Lattice.HeytingAlgebra._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_1724 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_1724 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_HeytingAlgebra_1602
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_1724 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3
  = T_HeytingAlgebra_1602
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_1724 T_HeytingAlgebra_1602
v3
du_'8764''45'resp'737''45''8776'_1724 ::
  T_HeytingAlgebra_1602 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_1724 :: T_HeytingAlgebra_1602
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_1724 T_HeytingAlgebra_1602
v0
  = let v1 :: t
v1 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_1226
v2 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (AgdaAny -> T_BoundedLattice_1324
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_810
v3 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_162
v4 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_100
                  ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                     (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v4))))))
-- Relation.Binary.Lattice.HeytingAlgebra._.Eq.isPartialEquivalence
d_isPartialEquivalence_1728 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1728 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_HeytingAlgebra_1602
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1728 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3
  = T_HeytingAlgebra_1602 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1728 T_HeytingAlgebra_1602
v3
du_isPartialEquivalence_1728 ::
  T_HeytingAlgebra_1602 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1728 :: T_HeytingAlgebra_1602 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1728 T_HeytingAlgebra_1602
v0
  = let v1 :: t
v1 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_1226
v2 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (AgdaAny -> T_BoundedLattice_1324
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_810
v3 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_162
v4 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPreorder_70
v5
                      = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                          (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                     ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                        (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v5)))))))
-- Relation.Binary.Lattice.HeytingAlgebra._.Eq.refl
d_refl_1730 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny
d_refl_1730 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_HeytingAlgebra_1602
-> AgdaAny
-> AgdaAny
d_refl_1730 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3 = T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny
du_refl_1730 T_HeytingAlgebra_1602
v3
du_refl_1730 :: T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny
du_refl_1730 :: T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny
du_refl_1730 T_HeytingAlgebra_1602
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
               ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254
                  ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1644 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0)))))))
-- Relation.Binary.Lattice.HeytingAlgebra._.Eq.reflexive
d_reflexive_1732 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1732 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_HeytingAlgebra_1602
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1732 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3 = T_HeytingAlgebra_1602
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1732 T_HeytingAlgebra_1602
v3
du_reflexive_1732 ::
  T_HeytingAlgebra_1602 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1732 :: T_HeytingAlgebra_1602
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1732 T_HeytingAlgebra_1602
v0
  = let v1 :: t
v1 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_1226
v2 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (AgdaAny -> T_BoundedLattice_1324
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_810
v3 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_162
v4 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPreorder_70
v5
                      = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                          (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
v4) in
                (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                  (\ AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 ->
                     (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                       ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                          (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v5))
                       AgdaAny
v6)))))
-- Relation.Binary.Lattice.HeytingAlgebra._.Eq.sym
d_sym_1734 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1734 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_HeytingAlgebra_1602
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_1734 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3 = T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1734 T_HeytingAlgebra_1602
v3
du_sym_1734 ::
  T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1734 :: T_HeytingAlgebra_1602 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_1734 T_HeytingAlgebra_1602
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
               ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254
                  ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1644 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0)))))))
-- Relation.Binary.Lattice.HeytingAlgebra._.Eq.trans
d_trans_1736 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_HeytingAlgebra_1602 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1736 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_HeytingAlgebra_1602
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_1736 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_HeytingAlgebra_1602
v3 = T_HeytingAlgebra_1602
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1736 T_HeytingAlgebra_1602
v3
du_trans_1736 ::
  T_HeytingAlgebra_1602 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1736 :: T_HeytingAlgebra_1602
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1736 T_HeytingAlgebra_1602
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
               ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254
                  ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1644 (T_HeytingAlgebra_1602 -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602
v0)))))))
-- Relation.Binary.Lattice.IsBooleanAlgebra
d_IsBooleanAlgebra_1760 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> T_Level_18
d_IsBooleanAlgebra_1760 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 p
a9 p
a10 = ()
newtype T_IsBooleanAlgebra_1760
  = C_IsBooleanAlgebra'46'constructor_59449 T_IsHeytingAlgebra_1468
-- Relation.Binary.Lattice.IsBooleanAlgebra._⇨_
d__'8680'__1792 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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) ->
  AgdaAny ->
  AgdaAny -> T_IsBooleanAlgebra_1760 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8680'__1792 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_1760
-> AgdaAny
-> AgdaAny
-> AgdaAny
d__'8680'__1792 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10 ~T_IsBooleanAlgebra_1760
v11 AgdaAny
v12
                AgdaAny
v13
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'8680'__1792 AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny -> AgdaAny
v8 AgdaAny
v12 AgdaAny
v13
du__'8680'__1792 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'8680'__1792 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'8680'__1792 AgdaAny -> AgdaAny -> AgdaAny
v0 AgdaAny -> AgdaAny
v1 AgdaAny
v2 AgdaAny
v3 = (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0 ((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v1 AgdaAny
v2) AgdaAny
v3
-- Relation.Binary.Lattice.IsBooleanAlgebra.isHeytingAlgebra
d_isHeytingAlgebra_1798 ::
  T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1798 :: T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1798 T_IsBooleanAlgebra_1760
v0
  = case T_IsBooleanAlgebra_1760 -> T_IsBooleanAlgebra_1760
forall a b. a -> b
coe T_IsBooleanAlgebra_1760
v0 of
      C_IsBooleanAlgebra'46'constructor_59449 T_IsHeytingAlgebra_1468
v1 -> T_IsHeytingAlgebra_1468 -> T_IsHeytingAlgebra_1468
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v1
      T_IsBooleanAlgebra_1760
_ -> T_IsHeytingAlgebra_1468
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.IsBooleanAlgebra._.antisym
d_antisym_1802 ::
  T_IsBooleanAlgebra_1760 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_1802 :: T_IsBooleanAlgebra_1760
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_1802 T_IsBooleanAlgebra_1760
v0
  = (T_IsPartialOrder_162
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_162
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_172
      ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
         ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254
            ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1798 (T_IsBooleanAlgebra_1760 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1760
v0)))))
-- Relation.Binary.Lattice.IsBooleanAlgebra._.exponential
d_exponential_1804 ::
  T_IsBooleanAlgebra_1760 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_exponential_1804 :: T_IsBooleanAlgebra_1760 -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
d_exponential_1804 T_IsBooleanAlgebra_1760
v0
  = (T_IsHeytingAlgebra_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsHeytingAlgebra_1468 -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
d_exponential_1498 ((T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1798 (T_IsBooleanAlgebra_1760 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1760
v0))
-- Relation.Binary.Lattice.IsBooleanAlgebra._.infimum
d_infimum_1806 ::
  T_IsBooleanAlgebra_1760 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_infimum_1806 :: T_IsBooleanAlgebra_1760 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_1806 T_IsBooleanAlgebra_1760
v0
  = (T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_838
      ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254
         ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1798 (T_IsBooleanAlgebra_1760 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1760
v0))))
-- Relation.Binary.Lattice.IsBooleanAlgebra._.isBoundedJoinSemilattice
d_isBoundedJoinSemilattice_1808 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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) ->
  AgdaAny ->
  AgdaAny ->
  T_IsBooleanAlgebra_1760 -> T_IsBoundedJoinSemilattice_262
d_isBoundedJoinSemilattice_1808 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_1760
-> T_IsBoundedJoinSemilattice_262
d_isBoundedJoinSemilattice_1808 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny
v8
                                ~AgdaAny
v9 ~AgdaAny
v10 T_IsBooleanAlgebra_1760
v11
  = T_IsBooleanAlgebra_1760 -> T_IsBoundedJoinSemilattice_262
du_isBoundedJoinSemilattice_1808 T_IsBooleanAlgebra_1760
v11
du_isBoundedJoinSemilattice_1808 ::
  T_IsBooleanAlgebra_1760 -> T_IsBoundedJoinSemilattice_262
du_isBoundedJoinSemilattice_1808 :: T_IsBooleanAlgebra_1760 -> T_IsBoundedJoinSemilattice_262
du_isBoundedJoinSemilattice_1808 T_IsBooleanAlgebra_1760
v0
  = let v1 :: T_IsHeytingAlgebra_1468
v1 = T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1798 (T_IsBooleanAlgebra_1760 -> T_IsBooleanAlgebra_1760
forall a b. a -> b
coe T_IsBooleanAlgebra_1760
v0) in
    AgdaAny -> T_IsBoundedJoinSemilattice_262
forall a b. a -> b
coe
      ((T_IsBoundedLattice_1226 -> T_IsBoundedJoinSemilattice_262)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBoundedLattice_1226 -> T_IsBoundedJoinSemilattice_262
du_isBoundedJoinSemilattice_1314
         ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v1)))
-- Relation.Binary.Lattice.IsBooleanAlgebra._.isBoundedLattice
d_isBoundedLattice_1810 ::
  T_IsBooleanAlgebra_1760 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1810 :: T_IsBooleanAlgebra_1760 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1810 T_IsBooleanAlgebra_1760
v0
  = (T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> T_IsBoundedLattice_1226
forall a b. a -> b
coe
      T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1798 (T_IsBooleanAlgebra_1760 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1760
v0))
-- Relation.Binary.Lattice.IsBooleanAlgebra._.isBoundedMeetSemilattice
d_isBoundedMeetSemilattice_1812 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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) ->
  AgdaAny ->
  AgdaAny ->
  T_IsBooleanAlgebra_1760 -> T_IsBoundedMeetSemilattice_632
d_isBoundedMeetSemilattice_1812 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_1760
-> T_IsBoundedMeetSemilattice_632
d_isBoundedMeetSemilattice_1812 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny
v8
                                ~AgdaAny
v9 ~AgdaAny
v10 T_IsBooleanAlgebra_1760
v11
  = T_IsBooleanAlgebra_1760 -> T_IsBoundedMeetSemilattice_632
du_isBoundedMeetSemilattice_1812 T_IsBooleanAlgebra_1760
v11
du_isBoundedMeetSemilattice_1812 ::
  T_IsBooleanAlgebra_1760 -> T_IsBoundedMeetSemilattice_632
du_isBoundedMeetSemilattice_1812 :: T_IsBooleanAlgebra_1760 -> T_IsBoundedMeetSemilattice_632
du_isBoundedMeetSemilattice_1812 T_IsBooleanAlgebra_1760
v0
  = let v1 :: T_IsHeytingAlgebra_1468
v1 = T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1798 (T_IsBooleanAlgebra_1760 -> T_IsBooleanAlgebra_1760
forall a b. a -> b
coe T_IsBooleanAlgebra_1760
v0) in
    AgdaAny -> T_IsBoundedMeetSemilattice_632
forall a b. a -> b
coe
      ((T_IsBoundedLattice_1226 -> T_IsBoundedMeetSemilattice_632)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBoundedLattice_1226 -> T_IsBoundedMeetSemilattice_632
du_isBoundedMeetSemilattice_1316
         ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v1)))
-- Relation.Binary.Lattice.IsBooleanAlgebra._.isEquivalence
d_isEquivalence_1814 ::
  T_IsBooleanAlgebra_1760 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1814 :: T_IsBooleanAlgebra_1760 -> T_IsEquivalence_26
d_isEquivalence_1814 T_IsBooleanAlgebra_1760
v0
  = (T_IsPreorder_70 -> T_IsEquivalence_26)
-> AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
            ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254
               ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1798 (T_IsBooleanAlgebra_1760 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1760
v0))))))
-- Relation.Binary.Lattice.IsBooleanAlgebra._.isJoinSemilattice
d_isJoinSemilattice_1816 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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) ->
  AgdaAny ->
  AgdaAny -> T_IsBooleanAlgebra_1760 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_1816 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_1760
-> T_IsJoinSemilattice_68
d_isJoinSemilattice_1816 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny
v9
                         ~AgdaAny
v10 T_IsBooleanAlgebra_1760
v11
  = T_IsBooleanAlgebra_1760 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_1816 T_IsBooleanAlgebra_1760
v11
du_isJoinSemilattice_1816 ::
  T_IsBooleanAlgebra_1760 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_1816 :: T_IsBooleanAlgebra_1760 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_1816 T_IsBooleanAlgebra_1760
v0
  = let v1 :: T_IsHeytingAlgebra_1468
v1 = T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1798 (T_IsBooleanAlgebra_1760 -> T_IsBooleanAlgebra_1760
forall a b. a -> b
coe T_IsBooleanAlgebra_1760
v0) in
    AgdaAny -> T_IsJoinSemilattice_68
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_1226
v2 = T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> T_IsHeytingAlgebra_1468
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsLattice_810 -> T_IsJoinSemilattice_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226
v2))))
-- Relation.Binary.Lattice.IsBooleanAlgebra._.isLattice
d_isLattice_1818 :: T_IsBooleanAlgebra_1760 -> T_IsLattice_810
d_isLattice_1818 :: T_IsBooleanAlgebra_1760 -> T_IsLattice_810
d_isLattice_1818 T_IsBooleanAlgebra_1760
v0
  = (T_IsBoundedLattice_1226 -> T_IsLattice_810)
-> AgdaAny -> T_IsLattice_810
forall a b. a -> b
coe
      T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254
      ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1798 (T_IsBooleanAlgebra_1760 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1760
v0)))
-- Relation.Binary.Lattice.IsBooleanAlgebra._.isMeetSemilattice
d_isMeetSemilattice_1820 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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) ->
  AgdaAny ->
  AgdaAny -> T_IsBooleanAlgebra_1760 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_1820 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_1760
-> T_IsMeetSemilattice_438
d_isMeetSemilattice_1820 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny
v9
                         ~AgdaAny
v10 T_IsBooleanAlgebra_1760
v11
  = T_IsBooleanAlgebra_1760 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_1820 T_IsBooleanAlgebra_1760
v11
du_isMeetSemilattice_1820 ::
  T_IsBooleanAlgebra_1760 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_1820 :: T_IsBooleanAlgebra_1760 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_1820 T_IsBooleanAlgebra_1760
v0
  = let v1 :: T_IsHeytingAlgebra_1468
v1 = T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1798 (T_IsBooleanAlgebra_1760 -> T_IsBooleanAlgebra_1760
forall a b. a -> b
coe T_IsBooleanAlgebra_1760
v0) in
    AgdaAny -> T_IsMeetSemilattice_438
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_1226
v2 = T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> T_IsHeytingAlgebra_1468
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsLattice_810 -> T_IsMeetSemilattice_438) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226
v2))))
-- Relation.Binary.Lattice.IsBooleanAlgebra._.isPartialOrder
d_isPartialOrder_1822 ::
  T_IsBooleanAlgebra_1760 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_162
d_isPartialOrder_1822 :: T_IsBooleanAlgebra_1760 -> T_IsPartialOrder_162
d_isPartialOrder_1822 T_IsBooleanAlgebra_1760
v0
  = (T_IsLattice_810 -> T_IsPartialOrder_162)
-> AgdaAny -> T_IsPartialOrder_162
forall a b. a -> b
coe
      T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
      ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254
         ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1798 (T_IsBooleanAlgebra_1760 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1760
v0))))
-- Relation.Binary.Lattice.IsBooleanAlgebra._.isPreorder
d_isPreorder_1824 ::
  T_IsBooleanAlgebra_1760 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_1824 :: T_IsBooleanAlgebra_1760 -> T_IsPreorder_70
d_isPreorder_1824 T_IsBooleanAlgebra_1760
v0
  = (T_IsPartialOrder_162 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
      ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
         ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254
            ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1798 (T_IsBooleanAlgebra_1760 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1760
v0)))))
-- Relation.Binary.Lattice.IsBooleanAlgebra._.maximum
d_maximum_1826 :: T_IsBooleanAlgebra_1760 -> AgdaAny -> AgdaAny
d_maximum_1826 :: T_IsBooleanAlgebra_1760 -> AgdaAny -> AgdaAny
d_maximum_1826 T_IsBooleanAlgebra_1760
v0
  = (T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny
d_maximum_1256
      ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1798 (T_IsBooleanAlgebra_1760 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1760
v0)))
-- Relation.Binary.Lattice.IsBooleanAlgebra._.minimum
d_minimum_1828 :: T_IsBooleanAlgebra_1760 -> AgdaAny -> AgdaAny
d_minimum_1828 :: T_IsBooleanAlgebra_1760 -> AgdaAny -> AgdaAny
d_minimum_1828 T_IsBooleanAlgebra_1760
v0
  = (T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny
d_minimum_1258
      ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1798 (T_IsBooleanAlgebra_1760 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1760
v0)))
-- Relation.Binary.Lattice.IsBooleanAlgebra._.refl
d_refl_1830 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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) ->
  AgdaAny -> AgdaAny -> T_IsBooleanAlgebra_1760 -> AgdaAny -> AgdaAny
d_refl_1830 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_1760
-> AgdaAny
-> AgdaAny
d_refl_1830 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10 T_IsBooleanAlgebra_1760
v11
  = T_IsBooleanAlgebra_1760 -> AgdaAny -> AgdaAny
du_refl_1830 T_IsBooleanAlgebra_1760
v11
du_refl_1830 :: T_IsBooleanAlgebra_1760 -> AgdaAny -> AgdaAny
du_refl_1830 :: T_IsBooleanAlgebra_1760 -> AgdaAny -> AgdaAny
du_refl_1830 T_IsBooleanAlgebra_1760
v0
  = let v1 :: T_IsHeytingAlgebra_1468
v1 = T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1798 (T_IsBooleanAlgebra_1760 -> T_IsBooleanAlgebra_1760
forall a b. a -> b
coe T_IsBooleanAlgebra_1760
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_1226
v2 = T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> T_IsHeytingAlgebra_1468
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_810
v3 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_162
v4 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsPreorder_70 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_70 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_98
                  ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                     (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v4))))))
-- Relation.Binary.Lattice.IsBooleanAlgebra._.reflexive
d_reflexive_1832 ::
  T_IsBooleanAlgebra_1760 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_1832 :: T_IsBooleanAlgebra_1760 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_1832 T_IsBooleanAlgebra_1760
v0
  = (T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
            ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254
               ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1798 (T_IsBooleanAlgebra_1760 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1760
v0))))))
-- Relation.Binary.Lattice.IsBooleanAlgebra._.supremum
d_supremum_1834 ::
  T_IsBooleanAlgebra_1760 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_supremum_1834 :: T_IsBooleanAlgebra_1760 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_1834 T_IsBooleanAlgebra_1760
v0
  = (T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_836
      ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254
         ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1798 (T_IsBooleanAlgebra_1760 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1760
v0))))
-- Relation.Binary.Lattice.IsBooleanAlgebra._.trans
d_trans_1836 ::
  T_IsBooleanAlgebra_1760 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1836 :: T_IsBooleanAlgebra_1760
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1836 T_IsBooleanAlgebra_1760
v0
  = (T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
            ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254
               ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1798 (T_IsBooleanAlgebra_1760 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1760
v0))))))
-- Relation.Binary.Lattice.IsBooleanAlgebra._.transpose-⇨
d_transpose'45''8680'_1838 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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) ->
  AgdaAny ->
  AgdaAny ->
  T_IsBooleanAlgebra_1760 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_transpose'45''8680'_1838 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_1760
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_transpose'45''8680'_1838 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny
v9
                           ~AgdaAny
v10 T_IsBooleanAlgebra_1760
v11
  = T_IsBooleanAlgebra_1760
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8680'_1838 T_IsBooleanAlgebra_1760
v11
du_transpose'45''8680'_1838 ::
  T_IsBooleanAlgebra_1760 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8680'_1838 :: T_IsBooleanAlgebra_1760
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8680'_1838 T_IsBooleanAlgebra_1760
v0
  = (T_IsHeytingAlgebra_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsHeytingAlgebra_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8680'_1506 ((T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1798 (T_IsBooleanAlgebra_1760 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1760
v0))
-- Relation.Binary.Lattice.IsBooleanAlgebra._.transpose-∧
d_transpose'45''8743'_1840 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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) ->
  AgdaAny ->
  AgdaAny ->
  T_IsBooleanAlgebra_1760 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_transpose'45''8743'_1840 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_1760
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_transpose'45''8743'_1840 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny
v9
                           ~AgdaAny
v10 T_IsBooleanAlgebra_1760
v11
  = T_IsBooleanAlgebra_1760
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8743'_1840 T_IsBooleanAlgebra_1760
v11
du_transpose'45''8743'_1840 ::
  T_IsBooleanAlgebra_1760 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8743'_1840 :: T_IsBooleanAlgebra_1760
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8743'_1840 T_IsBooleanAlgebra_1760
v0
  = (T_IsHeytingAlgebra_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsHeytingAlgebra_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8743'_1522 ((T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1798 (T_IsBooleanAlgebra_1760 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1760
v0))
-- Relation.Binary.Lattice.IsBooleanAlgebra._.x∧y≤x
d_x'8743'y'8804'x_1842 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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) ->
  AgdaAny ->
  AgdaAny -> T_IsBooleanAlgebra_1760 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'x_1842 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_1760
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'x_1842 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10
                       T_IsBooleanAlgebra_1760
v11
  = T_IsBooleanAlgebra_1760 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_1842 T_IsBooleanAlgebra_1760
v11
du_x'8743'y'8804'x_1842 ::
  T_IsBooleanAlgebra_1760 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_1842 :: T_IsBooleanAlgebra_1760 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_1842 T_IsBooleanAlgebra_1760
v0
  = let v1 :: T_IsHeytingAlgebra_1468
v1 = T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1798 (T_IsBooleanAlgebra_1760 -> T_IsBooleanAlgebra_1760
forall a b. a -> b
coe T_IsBooleanAlgebra_1760
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_1226
v2 = T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> T_IsHeytingAlgebra_1468
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_810
v3 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_466 ((T_IsLattice_810 -> T_IsMeetSemilattice_438) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v3)))))
-- Relation.Binary.Lattice.IsBooleanAlgebra._.x∧y≤y
d_x'8743'y'8804'y_1844 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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) ->
  AgdaAny ->
  AgdaAny -> T_IsBooleanAlgebra_1760 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'y_1844 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_1760
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'y_1844 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10
                       T_IsBooleanAlgebra_1760
v11
  = T_IsBooleanAlgebra_1760 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_1844 T_IsBooleanAlgebra_1760
v11
du_x'8743'y'8804'y_1844 ::
  T_IsBooleanAlgebra_1760 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_1844 :: T_IsBooleanAlgebra_1760 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_1844 T_IsBooleanAlgebra_1760
v0
  = let v1 :: T_IsHeytingAlgebra_1468
v1 = T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1798 (T_IsBooleanAlgebra_1760 -> T_IsBooleanAlgebra_1760
forall a b. a -> b
coe T_IsBooleanAlgebra_1760
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_1226
v2 = T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> T_IsHeytingAlgebra_1468
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_810
v3 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_478 ((T_IsLattice_810 -> T_IsMeetSemilattice_438) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v3)))))
-- Relation.Binary.Lattice.IsBooleanAlgebra._.x≤x∨y
d_x'8804'x'8744'y_1846 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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) ->
  AgdaAny ->
  AgdaAny -> T_IsBooleanAlgebra_1760 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8804'x'8744'y_1846 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_1760
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8804'x'8744'y_1846 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10
                       T_IsBooleanAlgebra_1760
v11
  = T_IsBooleanAlgebra_1760 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_1846 T_IsBooleanAlgebra_1760
v11
du_x'8804'x'8744'y_1846 ::
  T_IsBooleanAlgebra_1760 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_1846 :: T_IsBooleanAlgebra_1760 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_1846 T_IsBooleanAlgebra_1760
v0
  = let v1 :: T_IsHeytingAlgebra_1468
v1 = T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1798 (T_IsBooleanAlgebra_1760 -> T_IsBooleanAlgebra_1760
forall a b. a -> b
coe T_IsBooleanAlgebra_1760
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_1226
v2 = T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> T_IsHeytingAlgebra_1468
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_810
v3 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_96 ((T_IsLattice_810 -> T_IsJoinSemilattice_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v3)))))
-- Relation.Binary.Lattice.IsBooleanAlgebra._.y≤x∨y
d_y'8804'x'8744'y_1848 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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) ->
  AgdaAny ->
  AgdaAny -> T_IsBooleanAlgebra_1760 -> AgdaAny -> AgdaAny -> AgdaAny
d_y'8804'x'8744'y_1848 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_1760
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_y'8804'x'8744'y_1848 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10
                       T_IsBooleanAlgebra_1760
v11
  = T_IsBooleanAlgebra_1760 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_1848 T_IsBooleanAlgebra_1760
v11
du_y'8804'x'8744'y_1848 ::
  T_IsBooleanAlgebra_1760 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_1848 :: T_IsBooleanAlgebra_1760 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_1848 T_IsBooleanAlgebra_1760
v0
  = let v1 :: T_IsHeytingAlgebra_1468
v1 = T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1798 (T_IsBooleanAlgebra_1760 -> T_IsBooleanAlgebra_1760
forall a b. a -> b
coe T_IsBooleanAlgebra_1760
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_1226
v2 = T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> T_IsHeytingAlgebra_1468
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_810
v3 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_108 ((T_IsLattice_810 -> T_IsJoinSemilattice_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v3)))))
-- Relation.Binary.Lattice.IsBooleanAlgebra._.∧-greatest
d_'8743''45'greatest_1850 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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) ->
  AgdaAny ->
  AgdaAny ->
  T_IsBooleanAlgebra_1760 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'greatest_1850 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_1760
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'greatest_1850 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny
v9
                          ~AgdaAny
v10 T_IsBooleanAlgebra_1760
v11
  = T_IsBooleanAlgebra_1760
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_1850 T_IsBooleanAlgebra_1760
v11
du_'8743''45'greatest_1850 ::
  T_IsBooleanAlgebra_1760 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_1850 :: T_IsBooleanAlgebra_1760
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_1850 T_IsBooleanAlgebra_1760
v0
  = let v1 :: T_IsHeytingAlgebra_1468
v1 = T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1798 (T_IsBooleanAlgebra_1760 -> T_IsBooleanAlgebra_1760
forall a b. a -> b
coe T_IsBooleanAlgebra_1760
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_1226
v2 = T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> T_IsHeytingAlgebra_1468
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_810
v3 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMeetSemilattice_438
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMeetSemilattice_438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_492
               ((T_IsLattice_810 -> T_IsMeetSemilattice_438) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v3)))))
-- Relation.Binary.Lattice.IsBooleanAlgebra._.∨-least
d_'8744''45'least_1852 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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) ->
  AgdaAny ->
  AgdaAny ->
  T_IsBooleanAlgebra_1760 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'least_1852 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_1760
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'least_1852 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10
                       T_IsBooleanAlgebra_1760
v11
  = T_IsBooleanAlgebra_1760
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_1852 T_IsBooleanAlgebra_1760
v11
du_'8744''45'least_1852 ::
  T_IsBooleanAlgebra_1760 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_1852 :: T_IsBooleanAlgebra_1760
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_1852 T_IsBooleanAlgebra_1760
v0
  = let v1 :: T_IsHeytingAlgebra_1468
v1 = T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1798 (T_IsBooleanAlgebra_1760 -> T_IsBooleanAlgebra_1760
forall a b. a -> b
coe T_IsBooleanAlgebra_1760
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_1226
v2 = T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> T_IsHeytingAlgebra_1468
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_810
v3 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsJoinSemilattice_68
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsJoinSemilattice_68
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_122 ((T_IsLattice_810 -> T_IsJoinSemilattice_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v3)))))
-- Relation.Binary.Lattice.IsBooleanAlgebra._.∼-resp-≈
d_'8764''45'resp'45''8776'_1854 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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) ->
  AgdaAny ->
  AgdaAny ->
  T_IsBooleanAlgebra_1760 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_1854 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_1760
-> T_Σ_14
d_'8764''45'resp'45''8776'_1854 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny
v8
                                ~AgdaAny
v9 ~AgdaAny
v10 T_IsBooleanAlgebra_1760
v11
  = T_IsBooleanAlgebra_1760 -> T_Σ_14
du_'8764''45'resp'45''8776'_1854 T_IsBooleanAlgebra_1760
v11
du_'8764''45'resp'45''8776'_1854 ::
  T_IsBooleanAlgebra_1760 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_1854 :: T_IsBooleanAlgebra_1760 -> T_Σ_14
du_'8764''45'resp'45''8776'_1854 T_IsBooleanAlgebra_1760
v0
  = let v1 :: T_IsHeytingAlgebra_1468
v1 = T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1798 (T_IsBooleanAlgebra_1760 -> T_IsBooleanAlgebra_1760
forall a b. a -> b
coe T_IsBooleanAlgebra_1760
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_1226
v2 = T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> T_IsHeytingAlgebra_1468
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_810
v3 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_162
v4 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsPreorder_70 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_70 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_112
                  ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                     (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v4))))))
-- Relation.Binary.Lattice.IsBooleanAlgebra._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_1856 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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) ->
  AgdaAny ->
  AgdaAny ->
  T_IsBooleanAlgebra_1760 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_1856 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_1760
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_1856 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6
                                     ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10 T_IsBooleanAlgebra_1760
v11
  = T_IsBooleanAlgebra_1760
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_1856 T_IsBooleanAlgebra_1760
v11
du_'8764''45'resp'691''45''8776'_1856 ::
  T_IsBooleanAlgebra_1760 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_1856 :: T_IsBooleanAlgebra_1760
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_1856 T_IsBooleanAlgebra_1760
v0
  = let v1 :: T_IsHeytingAlgebra_1468
v1 = T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1798 (T_IsBooleanAlgebra_1760 -> T_IsBooleanAlgebra_1760
forall a b. a -> b
coe T_IsBooleanAlgebra_1760
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_1226
v2 = T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> T_IsHeytingAlgebra_1468
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_810
v3 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_162
v4 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_106
                  ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                     (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v4))))))
-- Relation.Binary.Lattice.IsBooleanAlgebra._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_1858 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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) ->
  AgdaAny ->
  AgdaAny ->
  T_IsBooleanAlgebra_1760 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_1858 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_1760
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_1858 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6
                                     ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10 T_IsBooleanAlgebra_1760
v11
  = T_IsBooleanAlgebra_1760
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_1858 T_IsBooleanAlgebra_1760
v11
du_'8764''45'resp'737''45''8776'_1858 ::
  T_IsBooleanAlgebra_1760 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_1858 :: T_IsBooleanAlgebra_1760
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_1858 T_IsBooleanAlgebra_1760
v0
  = let v1 :: T_IsHeytingAlgebra_1468
v1 = T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1798 (T_IsBooleanAlgebra_1760 -> T_IsBooleanAlgebra_1760
forall a b. a -> b
coe T_IsBooleanAlgebra_1760
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_1226
v2 = T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> T_IsHeytingAlgebra_1468
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_810
v3 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_162
v4 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_100
                  ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                     (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v4))))))
-- Relation.Binary.Lattice.IsBooleanAlgebra._.Eq.isPartialEquivalence
d_isPartialEquivalence_1862 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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) ->
  AgdaAny ->
  AgdaAny ->
  T_IsBooleanAlgebra_1760 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_1862 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_1760
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_1862 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny
v9
                            ~AgdaAny
v10 T_IsBooleanAlgebra_1760
v11
  = T_IsBooleanAlgebra_1760 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1862 T_IsBooleanAlgebra_1760
v11
du_isPartialEquivalence_1862 ::
  T_IsBooleanAlgebra_1760 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_1862 :: T_IsBooleanAlgebra_1760 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_1862 T_IsBooleanAlgebra_1760
v0
  = let v1 :: T_IsHeytingAlgebra_1468
v1 = T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1798 (T_IsBooleanAlgebra_1760 -> T_IsBooleanAlgebra_1760
forall a b. a -> b
coe T_IsBooleanAlgebra_1760
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_1226
v2 = T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> T_IsHeytingAlgebra_1468
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_810
v3 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_162
v4 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPreorder_70
v5
                      = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                          (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsEquivalence_26 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_26 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_42
                     ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                        (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v5)))))))
-- Relation.Binary.Lattice.IsBooleanAlgebra._.Eq.refl
d_refl_1864 :: T_IsBooleanAlgebra_1760 -> AgdaAny -> AgdaAny
d_refl_1864 :: T_IsBooleanAlgebra_1760 -> AgdaAny -> AgdaAny
d_refl_1864 T_IsBooleanAlgebra_1760
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
               ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254
                  ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1798 (T_IsBooleanAlgebra_1760 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1760
v0)))))))
-- Relation.Binary.Lattice.IsBooleanAlgebra._.Eq.reflexive
d_reflexive_1866 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  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) ->
  AgdaAny ->
  AgdaAny ->
  T_IsBooleanAlgebra_1760 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_1866 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_Level_18
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> T_Level_18)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_1760
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_1866 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 ~T_Level_18
v3 ~AgdaAny -> AgdaAny -> T_Level_18
v4 ~AgdaAny -> AgdaAny -> T_Level_18
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10 T_IsBooleanAlgebra_1760
v11
  = T_IsBooleanAlgebra_1760
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1866 T_IsBooleanAlgebra_1760
v11
du_reflexive_1866 ::
  T_IsBooleanAlgebra_1760 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_1866 :: T_IsBooleanAlgebra_1760
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_1866 T_IsBooleanAlgebra_1760
v0
  = let v1 :: T_IsHeytingAlgebra_1468
v1 = T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1798 (T_IsBooleanAlgebra_1760 -> T_IsBooleanAlgebra_1760
forall a b. a -> b
coe T_IsBooleanAlgebra_1760
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_1226
v2 = T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 (T_IsHeytingAlgebra_1468 -> T_IsHeytingAlgebra_1468
forall a b. a -> b
coe T_IsHeytingAlgebra_1468
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_810
v3 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_162
v4 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPreorder_70
v5
                      = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                          (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
v4) in
                (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                  (\ AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 ->
                     (T_IsEquivalence_26 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsEquivalence_26 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_40
                       ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                          (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v5))
                       AgdaAny
v6)))))
-- Relation.Binary.Lattice.IsBooleanAlgebra._.Eq.sym
d_sym_1868 ::
  T_IsBooleanAlgebra_1760 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1868 :: T_IsBooleanAlgebra_1760 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_1868 T_IsBooleanAlgebra_1760
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
               ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254
                  ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1798 (T_IsBooleanAlgebra_1760 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1760
v0)))))))
-- Relation.Binary.Lattice.IsBooleanAlgebra._.Eq.trans
d_trans_1870 ::
  T_IsBooleanAlgebra_1760 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1870 :: T_IsBooleanAlgebra_1760
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1870 T_IsBooleanAlgebra_1760
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
               ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254
                  ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1798 (T_IsBooleanAlgebra_1760 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_1760
v0)))))))
-- Relation.Binary.Lattice.BooleanAlgebra
d_BooleanAlgebra_1878 :: p -> p -> p -> T_Level_18
d_BooleanAlgebra_1878 p
a0 p
a1 p
a2 = ()
data T_BooleanAlgebra_1878
  = C_BooleanAlgebra'46'constructor_65119 (AgdaAny ->
                                           AgdaAny -> AgdaAny)
                                          (AgdaAny -> AgdaAny -> AgdaAny) (AgdaAny -> AgdaAny)
                                          AgdaAny AgdaAny T_IsBooleanAlgebra_1760
-- Relation.Binary.Lattice.BooleanAlgebra.Carrier
d_Carrier_1904 :: T_BooleanAlgebra_1878 -> ()
d_Carrier_1904 :: T_BooleanAlgebra_1878 -> T_Level_18
d_Carrier_1904 = T_BooleanAlgebra_1878 -> T_Level_18
forall a. a
erased
-- Relation.Binary.Lattice.BooleanAlgebra._≈_
d__'8776'__1906 ::
  T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> ()
d__'8776'__1906 :: T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> T_Level_18
d__'8776'__1906 = T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> T_Level_18
forall a. a
erased
-- Relation.Binary.Lattice.BooleanAlgebra._≤_
d__'8804'__1908 ::
  T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> ()
d__'8804'__1908 :: T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> T_Level_18
d__'8804'__1908 = T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> T_Level_18
forall a. a
erased
-- Relation.Binary.Lattice.BooleanAlgebra._∨_
d__'8744'__1910 ::
  T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__1910 :: T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__1910 T_BooleanAlgebra_1878
v0
  = case T_BooleanAlgebra_1878 -> T_BooleanAlgebra_1878
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0 of
      C_BooleanAlgebra'46'constructor_65119 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 T_IsBooleanAlgebra_1760
v9 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v4
      T_BooleanAlgebra_1878
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.BooleanAlgebra._∧_
d__'8743'__1912 ::
  T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__1912 :: T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__1912 T_BooleanAlgebra_1878
v0
  = case T_BooleanAlgebra_1878 -> T_BooleanAlgebra_1878
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0 of
      C_BooleanAlgebra'46'constructor_65119 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 T_IsBooleanAlgebra_1760
v9 -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v5
      T_BooleanAlgebra_1878
_ -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.BooleanAlgebra.¬_
d_'172'__1914 :: T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny
d_'172'__1914 :: T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny
d_'172'__1914 T_BooleanAlgebra_1878
v0
  = case T_BooleanAlgebra_1878 -> T_BooleanAlgebra_1878
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0 of
      C_BooleanAlgebra'46'constructor_65119 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 T_IsBooleanAlgebra_1760
v9 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v6
      T_BooleanAlgebra_1878
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.BooleanAlgebra.⊤
d_'8868'_1916 :: T_BooleanAlgebra_1878 -> AgdaAny
d_'8868'_1916 :: T_BooleanAlgebra_1878 -> AgdaAny
d_'8868'_1916 T_BooleanAlgebra_1878
v0
  = case T_BooleanAlgebra_1878 -> T_BooleanAlgebra_1878
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0 of
      C_BooleanAlgebra'46'constructor_65119 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 T_IsBooleanAlgebra_1760
v9 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v7
      T_BooleanAlgebra_1878
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.BooleanAlgebra.⊥
d_'8869'_1918 :: T_BooleanAlgebra_1878 -> AgdaAny
d_'8869'_1918 :: T_BooleanAlgebra_1878 -> AgdaAny
d_'8869'_1918 T_BooleanAlgebra_1878
v0
  = case T_BooleanAlgebra_1878 -> T_BooleanAlgebra_1878
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0 of
      C_BooleanAlgebra'46'constructor_65119 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 T_IsBooleanAlgebra_1760
v9 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v8
      T_BooleanAlgebra_1878
_ -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.BooleanAlgebra.isBooleanAlgebra
d_isBooleanAlgebra_1920 ::
  T_BooleanAlgebra_1878 -> T_IsBooleanAlgebra_1760
d_isBooleanAlgebra_1920 :: T_BooleanAlgebra_1878 -> T_IsBooleanAlgebra_1760
d_isBooleanAlgebra_1920 T_BooleanAlgebra_1878
v0
  = case T_BooleanAlgebra_1878 -> T_BooleanAlgebra_1878
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0 of
      C_BooleanAlgebra'46'constructor_65119 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny -> AgdaAny -> AgdaAny
v5 AgdaAny -> AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 T_IsBooleanAlgebra_1760
v9 -> T_IsBooleanAlgebra_1760 -> T_IsBooleanAlgebra_1760
forall a b. a -> b
coe T_IsBooleanAlgebra_1760
v9
      T_BooleanAlgebra_1878
_ -> T_IsBooleanAlgebra_1760
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.BooleanAlgebra._.isHeytingAlgebra
d_isHeytingAlgebra_1924 ::
  T_BooleanAlgebra_1878 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1924 :: T_BooleanAlgebra_1878 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1924 T_BooleanAlgebra_1878
v0
  = (T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> T_IsHeytingAlgebra_1468
forall a b. a -> b
coe
      T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1798 ((T_BooleanAlgebra_1878 -> T_IsBooleanAlgebra_1760)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_IsBooleanAlgebra_1760
d_isBooleanAlgebra_1920 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0))
-- Relation.Binary.Lattice.BooleanAlgebra.heytingAlgebra
d_heytingAlgebra_1926 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
d_heytingAlgebra_1926 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> T_HeytingAlgebra_1602
d_heytingAlgebra_1926 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3 = T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 T_BooleanAlgebra_1878
v3
du_heytingAlgebra_1926 ::
  T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 :: T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 T_BooleanAlgebra_1878
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> T_IsHeytingAlgebra_1468
 -> T_HeytingAlgebra_1602)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_1468
-> T_HeytingAlgebra_1602
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_1468
-> T_HeytingAlgebra_1602
C_HeytingAlgebra'46'constructor_55523 (T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__1910 (T_BooleanAlgebra_1878 -> T_BooleanAlgebra_1878
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0))
      (T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8743'__1912 (T_BooleanAlgebra_1878 -> T_BooleanAlgebra_1878
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0))
      (\ AgdaAny
v1 -> (T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__1910 T_BooleanAlgebra_1878
v0 ((T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny
d_'172'__1914 T_BooleanAlgebra_1878
v0 AgdaAny
v1))
      (T_BooleanAlgebra_1878 -> AgdaAny
d_'8868'_1916 (T_BooleanAlgebra_1878 -> T_BooleanAlgebra_1878
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0)) (T_BooleanAlgebra_1878 -> AgdaAny
d_'8869'_1918 (T_BooleanAlgebra_1878 -> T_BooleanAlgebra_1878
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0))
      (T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1798 ((T_BooleanAlgebra_1878 -> T_IsBooleanAlgebra_1760)
-> AgdaAny -> T_IsBooleanAlgebra_1760
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_IsBooleanAlgebra_1760
d_isBooleanAlgebra_1920 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0)))
-- Relation.Binary.Lattice.BooleanAlgebra._._⇨_
d__'8680'__1930 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8680'__1930 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> AgdaAny
-> AgdaAny
-> AgdaAny
d__'8680'__1930 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3 AgdaAny
v4 = T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny
du__'8680'__1930 T_BooleanAlgebra_1878
v3 AgdaAny
v4
du__'8680'__1930 ::
  T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny
du__'8680'__1930 :: T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny
du__'8680'__1930 T_BooleanAlgebra_1878
v0 AgdaAny
v1
  = (T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8744'__1910 T_BooleanAlgebra_1878
v0 ((T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny
d_'172'__1914 T_BooleanAlgebra_1878
v0 AgdaAny
v1)
-- Relation.Binary.Lattice.BooleanAlgebra._.antisym
d_antisym_1932 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_1932 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_antisym_1932 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3 = T_BooleanAlgebra_1878
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_antisym_1932 T_BooleanAlgebra_1878
v3
du_antisym_1932 ::
  T_BooleanAlgebra_1878 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_antisym_1932 :: T_BooleanAlgebra_1878
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_antisym_1932 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsPartialOrder_162
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_172
         ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
            ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254
               ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1644 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1))))))
-- Relation.Binary.Lattice.BooleanAlgebra._.boundedJoinSemilattice
d_boundedJoinSemilattice_1934 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 -> T_BoundedJoinSemilattice_336
d_boundedJoinSemilattice_1934 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> T_BoundedJoinSemilattice_336
d_boundedJoinSemilattice_1934 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3
  = T_BooleanAlgebra_1878 -> T_BoundedJoinSemilattice_336
du_boundedJoinSemilattice_1934 T_BooleanAlgebra_1878
v3
du_boundedJoinSemilattice_1934 ::
  T_BooleanAlgebra_1878 -> T_BoundedJoinSemilattice_336
du_boundedJoinSemilattice_1934 :: T_BooleanAlgebra_1878 -> T_BoundedJoinSemilattice_336
du_boundedJoinSemilattice_1934 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0) in
    AgdaAny -> T_BoundedJoinSemilattice_336
forall a b. a -> b
coe
      ((T_BoundedLattice_1324 -> T_BoundedJoinSemilattice_336)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_BoundedLattice_1324 -> T_BoundedJoinSemilattice_336
du_boundedJoinSemilattice_1428
         ((T_HeytingAlgebra_1602 -> T_BoundedLattice_1324)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Relation.Binary.Lattice.BooleanAlgebra._.boundedLattice
d_boundedLattice_1936 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 -> T_BoundedLattice_1324
d_boundedLattice_1936 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> T_BoundedLattice_1324
d_boundedLattice_1936 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3 = T_BooleanAlgebra_1878 -> T_BoundedLattice_1324
du_boundedLattice_1936 T_BooleanAlgebra_1878
v3
du_boundedLattice_1936 ::
  T_BooleanAlgebra_1878 -> T_BoundedLattice_1324
du_boundedLattice_1936 :: T_BooleanAlgebra_1878 -> T_BoundedLattice_1324
du_boundedLattice_1936 T_BooleanAlgebra_1878
v0
  = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324)
-> AgdaAny -> T_BoundedLattice_1324
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 ((T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0))
-- Relation.Binary.Lattice.BooleanAlgebra._.boundedMeetSemilattice
d_boundedMeetSemilattice_1938 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 -> T_BoundedMeetSemilattice_706
d_boundedMeetSemilattice_1938 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> T_BoundedMeetSemilattice_706
d_boundedMeetSemilattice_1938 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3
  = T_BooleanAlgebra_1878 -> T_BoundedMeetSemilattice_706
du_boundedMeetSemilattice_1938 T_BooleanAlgebra_1878
v3
du_boundedMeetSemilattice_1938 ::
  T_BooleanAlgebra_1878 -> T_BoundedMeetSemilattice_706
du_boundedMeetSemilattice_1938 :: T_BooleanAlgebra_1878 -> T_BoundedMeetSemilattice_706
du_boundedMeetSemilattice_1938 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0) in
    AgdaAny -> T_BoundedMeetSemilattice_706
forall a b. a -> b
coe
      ((T_BoundedLattice_1324 -> T_BoundedMeetSemilattice_706)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_BoundedLattice_1324 -> T_BoundedMeetSemilattice_706
du_boundedMeetSemilattice_1430
         ((T_HeytingAlgebra_1602 -> T_BoundedLattice_1324)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Relation.Binary.Lattice.BooleanAlgebra._.exponential
d_exponential_1940 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_exponential_1940 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_Σ_14
d_exponential_1940 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3 = T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
du_exponential_1940 T_BooleanAlgebra_1878
v3
du_exponential_1940 ::
  T_BooleanAlgebra_1878 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_exponential_1940 :: T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
du_exponential_1940 T_BooleanAlgebra_1878
v0
  = (T_IsHeytingAlgebra_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsHeytingAlgebra_1468 -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
d_exponential_1498
      ((T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1798 ((T_BooleanAlgebra_1878 -> T_IsBooleanAlgebra_1760)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_IsBooleanAlgebra_1760
d_isBooleanAlgebra_1920 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0)))
-- Relation.Binary.Lattice.BooleanAlgebra._.infimum
d_infimum_1942 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_infimum_1942 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> AgdaAny
-> AgdaAny
-> T_Σ_14
d_infimum_1942 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3 = T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> T_Σ_14
du_infimum_1942 T_BooleanAlgebra_1878
v3
du_infimum_1942 ::
  T_BooleanAlgebra_1878 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_infimum_1942 :: T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> T_Σ_14
du_infimum_1942 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      ((T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_838
         ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254
            ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1644 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))))
-- Relation.Binary.Lattice.BooleanAlgebra._.isBoundedJoinSemilattice
d_isBoundedJoinSemilattice_1944 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 -> T_IsBoundedJoinSemilattice_262
d_isBoundedJoinSemilattice_1944 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> T_IsBoundedJoinSemilattice_262
d_isBoundedJoinSemilattice_1944 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3
  = T_BooleanAlgebra_1878 -> T_IsBoundedJoinSemilattice_262
du_isBoundedJoinSemilattice_1944 T_BooleanAlgebra_1878
v3
du_isBoundedJoinSemilattice_1944 ::
  T_BooleanAlgebra_1878 -> T_IsBoundedJoinSemilattice_262
du_isBoundedJoinSemilattice_1944 :: T_BooleanAlgebra_1878 -> T_IsBoundedJoinSemilattice_262
du_isBoundedJoinSemilattice_1944 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0) in
    AgdaAny -> T_IsBoundedJoinSemilattice_262
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsBoundedLattice_1226 -> T_IsBoundedJoinSemilattice_262)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBoundedLattice_1226 -> T_IsBoundedJoinSemilattice_262
du_isBoundedJoinSemilattice_1314
            ((T_BoundedLattice_1324 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Relation.Binary.Lattice.BooleanAlgebra._.isBoundedLattice
d_isBoundedLattice_1946 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1946 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> T_IsBoundedLattice_1226
d_isBoundedLattice_1946 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3
  = T_BooleanAlgebra_1878 -> T_IsBoundedLattice_1226
du_isBoundedLattice_1946 T_BooleanAlgebra_1878
v3
du_isBoundedLattice_1946 ::
  T_BooleanAlgebra_1878 -> T_IsBoundedLattice_1226
du_isBoundedLattice_1946 :: T_BooleanAlgebra_1878 -> T_IsBoundedLattice_1226
du_isBoundedLattice_1946 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0) in
    AgdaAny -> T_IsBoundedLattice_1226
forall a b. a -> b
coe
      ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1644 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Relation.Binary.Lattice.BooleanAlgebra._.isBoundedMeetSemilattice
d_isBoundedMeetSemilattice_1948 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 -> T_IsBoundedMeetSemilattice_632
d_isBoundedMeetSemilattice_1948 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> T_IsBoundedMeetSemilattice_632
d_isBoundedMeetSemilattice_1948 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3
  = T_BooleanAlgebra_1878 -> T_IsBoundedMeetSemilattice_632
du_isBoundedMeetSemilattice_1948 T_BooleanAlgebra_1878
v3
du_isBoundedMeetSemilattice_1948 ::
  T_BooleanAlgebra_1878 -> T_IsBoundedMeetSemilattice_632
du_isBoundedMeetSemilattice_1948 :: T_BooleanAlgebra_1878 -> T_IsBoundedMeetSemilattice_632
du_isBoundedMeetSemilattice_1948 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0) in
    AgdaAny -> T_IsBoundedMeetSemilattice_632
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsBoundedLattice_1226 -> T_IsBoundedMeetSemilattice_632)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBoundedLattice_1226 -> T_IsBoundedMeetSemilattice_632
du_isBoundedMeetSemilattice_1316
            ((T_BoundedLattice_1324 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Relation.Binary.Lattice.BooleanAlgebra._.isEquivalence
d_isEquivalence_1950 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_1950 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> T_IsEquivalence_26
d_isEquivalence_1950 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3 = T_BooleanAlgebra_1878 -> T_IsEquivalence_26
du_isEquivalence_1950 T_BooleanAlgebra_1878
v3
du_isEquivalence_1950 ::
  T_BooleanAlgebra_1878 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
du_isEquivalence_1950 :: T_BooleanAlgebra_1878 -> T_IsEquivalence_26
du_isEquivalence_1950 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0) in
    AgdaAny -> T_IsEquivalence_26
forall a b. a -> b
coe
      ((T_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
               ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254
                  ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1644 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))))))
-- Relation.Binary.Lattice.BooleanAlgebra._.isHeytingAlgebra
d_isHeytingAlgebra_1952 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1952 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1952 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3
  = T_BooleanAlgebra_1878 -> T_IsHeytingAlgebra_1468
du_isHeytingAlgebra_1952 T_BooleanAlgebra_1878
v3
du_isHeytingAlgebra_1952 ::
  T_BooleanAlgebra_1878 -> T_IsHeytingAlgebra_1468
du_isHeytingAlgebra_1952 :: T_BooleanAlgebra_1878 -> T_IsHeytingAlgebra_1468
du_isHeytingAlgebra_1952 T_BooleanAlgebra_1878
v0
  = (T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> T_IsHeytingAlgebra_1468
forall a b. a -> b
coe
      T_IsBooleanAlgebra_1760 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1798 ((T_BooleanAlgebra_1878 -> T_IsBooleanAlgebra_1760)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_IsBooleanAlgebra_1760
d_isBooleanAlgebra_1920 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0))
-- Relation.Binary.Lattice.BooleanAlgebra._.isJoinSemilattice
d_isJoinSemilattice_1954 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 -> T_IsJoinSemilattice_68
d_isJoinSemilattice_1954 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> T_IsJoinSemilattice_68
d_isJoinSemilattice_1954 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3
  = T_BooleanAlgebra_1878 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_1954 T_BooleanAlgebra_1878
v3
du_isJoinSemilattice_1954 ::
  T_BooleanAlgebra_1878 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_1954 :: T_BooleanAlgebra_1878 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_1954 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0) in
    AgdaAny -> T_IsJoinSemilattice_68
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsBoundedLattice_1226
v3 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (AgdaAny -> T_BoundedLattice_1324
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsLattice_810 -> T_IsJoinSemilattice_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226
v3)))))
-- Relation.Binary.Lattice.BooleanAlgebra._.isLattice
d_isLattice_1956 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 -> T_IsLattice_810
d_isLattice_1956 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> T_IsLattice_810
d_isLattice_1956 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3 = T_BooleanAlgebra_1878 -> T_IsLattice_810
du_isLattice_1956 T_BooleanAlgebra_1878
v3
du_isLattice_1956 :: T_BooleanAlgebra_1878 -> T_IsLattice_810
du_isLattice_1956 :: T_BooleanAlgebra_1878 -> T_IsLattice_810
du_isLattice_1956 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0) in
    AgdaAny -> T_IsLattice_810
forall a b. a -> b
coe
      ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254
         ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1644 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1))))
-- Relation.Binary.Lattice.BooleanAlgebra._.isMeetSemilattice
d_isMeetSemilattice_1958 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 -> T_IsMeetSemilattice_438
d_isMeetSemilattice_1958 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> T_IsMeetSemilattice_438
d_isMeetSemilattice_1958 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3
  = T_BooleanAlgebra_1878 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_1958 T_BooleanAlgebra_1878
v3
du_isMeetSemilattice_1958 ::
  T_BooleanAlgebra_1878 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_1958 :: T_BooleanAlgebra_1878 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_1958 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0) in
    AgdaAny -> T_IsMeetSemilattice_438
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsBoundedLattice_1226
v3 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (AgdaAny -> T_BoundedLattice_1324
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsLattice_810 -> T_IsMeetSemilattice_438) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_1226
v3)))))
-- Relation.Binary.Lattice.BooleanAlgebra._.isPartialOrder
d_isPartialOrder_1960 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_162
d_isPartialOrder_1960 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> T_IsPartialOrder_162
d_isPartialOrder_1960 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3 = T_BooleanAlgebra_1878 -> T_IsPartialOrder_162
du_isPartialOrder_1960 T_BooleanAlgebra_1878
v3
du_isPartialOrder_1960 ::
  T_BooleanAlgebra_1878 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_162
du_isPartialOrder_1960 :: T_BooleanAlgebra_1878 -> T_IsPartialOrder_162
du_isPartialOrder_1960 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0) in
    AgdaAny -> T_IsPartialOrder_162
forall a b. a -> b
coe
      ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
         ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254
            ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1644 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))))
-- Relation.Binary.Lattice.BooleanAlgebra._.isPreorder
d_isPreorder_1962 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_1962 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> T_IsPreorder_70
d_isPreorder_1962 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3 = T_BooleanAlgebra_1878 -> T_IsPreorder_70
du_isPreorder_1962 T_BooleanAlgebra_1878
v3
du_isPreorder_1962 ::
  T_BooleanAlgebra_1878 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
du_isPreorder_1962 :: T_BooleanAlgebra_1878 -> T_IsPreorder_70
du_isPreorder_1962 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0) in
    AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
         ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
            ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254
               ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1644 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1))))))
-- Relation.Binary.Lattice.BooleanAlgebra._.joinSemilattice
d_joinSemilattice_1964 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 -> T_JoinSemilattice_170
d_joinSemilattice_1964 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> T_JoinSemilattice_170
d_joinSemilattice_1964 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3 = T_BooleanAlgebra_1878 -> T_JoinSemilattice_170
du_joinSemilattice_1964 T_BooleanAlgebra_1878
v3
du_joinSemilattice_1964 ::
  T_BooleanAlgebra_1878 -> T_JoinSemilattice_170
du_joinSemilattice_1964 :: T_BooleanAlgebra_1878 -> T_JoinSemilattice_170
du_joinSemilattice_1964 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0) in
    AgdaAny -> T_JoinSemilattice_170
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Lattice_898 -> T_JoinSemilattice_170) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_898 -> T_JoinSemilattice_170
du_joinSemilattice_986 ((T_BoundedLattice_1324 -> T_Lattice_898) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324 -> T_Lattice_898
du_lattice_1432 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Relation.Binary.Lattice.BooleanAlgebra._.lattice
d_lattice_1966 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 -> T_Lattice_898
d_lattice_1966 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> T_Lattice_898
d_lattice_1966 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3 = T_BooleanAlgebra_1878 -> T_Lattice_898
du_lattice_1966 T_BooleanAlgebra_1878
v3
du_lattice_1966 :: T_BooleanAlgebra_1878 -> T_Lattice_898
du_lattice_1966 :: T_BooleanAlgebra_1878 -> T_Lattice_898
du_lattice_1966 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0) in
    AgdaAny -> T_Lattice_898
forall a b. a -> b
coe ((T_BoundedLattice_1324 -> T_Lattice_898) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324 -> T_Lattice_898
du_lattice_1432 ((T_HeytingAlgebra_1602 -> T_BoundedLattice_1324)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Relation.Binary.Lattice.BooleanAlgebra._.maximum
d_maximum_1968 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny
d_maximum_1968 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> AgdaAny
-> AgdaAny
d_maximum_1968 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3 = T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny
du_maximum_1968 T_BooleanAlgebra_1878
v3
du_maximum_1968 :: T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny
du_maximum_1968 :: T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny
du_maximum_1968 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny
d_maximum_1256
         ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1644 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1))))
-- Relation.Binary.Lattice.BooleanAlgebra._.meetSemilattice
d_meetSemilattice_1970 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 -> T_MeetSemilattice_540
d_meetSemilattice_1970 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> T_MeetSemilattice_540
d_meetSemilattice_1970 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3 = T_BooleanAlgebra_1878 -> T_MeetSemilattice_540
du_meetSemilattice_1970 T_BooleanAlgebra_1878
v3
du_meetSemilattice_1970 ::
  T_BooleanAlgebra_1878 -> T_MeetSemilattice_540
du_meetSemilattice_1970 :: T_BooleanAlgebra_1878 -> T_MeetSemilattice_540
du_meetSemilattice_1970 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0) in
    AgdaAny -> T_MeetSemilattice_540
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Lattice_898 -> T_MeetSemilattice_540) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_898 -> T_MeetSemilattice_540
du_meetSemilattice_988 ((T_BoundedLattice_1324 -> T_Lattice_898) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324 -> T_Lattice_898
du_lattice_1432 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Relation.Binary.Lattice.BooleanAlgebra._.minimum
d_minimum_1972 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny
d_minimum_1972 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> AgdaAny
-> AgdaAny
d_minimum_1972 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3 = T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny
du_minimum_1972 T_BooleanAlgebra_1878
v3
du_minimum_1972 :: T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny
du_minimum_1972 :: T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny
du_minimum_1972 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBoundedLattice_1226 -> AgdaAny -> AgdaAny
d_minimum_1258
         ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1644 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1))))
-- Relation.Binary.Lattice.BooleanAlgebra._.poset
d_poset_1974 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Poset_282
d_poset_1974 :: T_Level_18
-> T_Level_18 -> T_Level_18 -> T_BooleanAlgebra_1878 -> T_Poset_282
d_poset_1974 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3 = T_BooleanAlgebra_1878 -> T_Poset_282
du_poset_1974 T_BooleanAlgebra_1878
v3
du_poset_1974 ::
  T_BooleanAlgebra_1878 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Poset_282
du_poset_1974 :: T_BooleanAlgebra_1878 -> T_Poset_282
du_poset_1974 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0) in
    AgdaAny -> T_Poset_282
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_BoundedLattice_1324 -> T_Lattice_898) -> AgdaAny -> t
forall a b. a -> b
coe T_BoundedLattice_1324 -> T_Lattice_898
du_lattice_1432 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_JoinSemilattice_170 -> T_Poset_282) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_170 -> T_Poset_282
du_poset_240 ((T_Lattice_898 -> T_JoinSemilattice_170) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_898 -> T_JoinSemilattice_170
du_joinSemilattice_986 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3)))))
-- Relation.Binary.Lattice.BooleanAlgebra._.preorder
d_preorder_1976 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Preorder_132
d_preorder_1976 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> T_Preorder_132
d_preorder_1976 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3 = T_BooleanAlgebra_1878 -> T_Preorder_132
du_preorder_1976 T_BooleanAlgebra_1878
v3
du_preorder_1976 ::
  T_BooleanAlgebra_1878 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Preorder_132
du_preorder_1976 :: T_BooleanAlgebra_1878 -> T_Preorder_132
du_preorder_1976 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0) in
    AgdaAny -> T_Preorder_132
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: t
v3 = (T_BoundedLattice_1324 -> T_Lattice_898) -> AgdaAny -> t
forall a b. a -> b
coe T_BoundedLattice_1324 -> T_Lattice_898
du_lattice_1432 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: t
v4 = (T_Lattice_898 -> T_JoinSemilattice_170) -> AgdaAny -> t
forall a b. a -> b
coe T_Lattice_898 -> T_JoinSemilattice_170
du_joinSemilattice_986 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_Poset_282 -> T_Preorder_132) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Poset_282 -> T_Preorder_132
MAlonzo.Code.Relation.Binary.Bundles.du_preorder_326
                  ((T_JoinSemilattice_170 -> T_Poset_282) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_JoinSemilattice_170 -> T_Poset_282
du_poset_240 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v4))))))
-- Relation.Binary.Lattice.BooleanAlgebra._.refl
d_refl_1978 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny
d_refl_1978 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> AgdaAny
-> AgdaAny
d_refl_1978 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3 = T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny
du_refl_1978 T_BooleanAlgebra_1878
v3
du_refl_1978 :: T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny
du_refl_1978 :: T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny
du_refl_1978 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsBoundedLattice_1226
v3 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (AgdaAny -> T_BoundedLattice_1324
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsLattice_810
v4 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_162
v5 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsPreorder_70 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPreorder_70 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_98
                     ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                        (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v5)))))))
-- Relation.Binary.Lattice.BooleanAlgebra._.reflexive
d_reflexive_1980 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_1980 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_reflexive_1980 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3 = T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_reflexive_1980 T_BooleanAlgebra_1878
v3
du_reflexive_1980 ::
  T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_reflexive_1980 :: T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_reflexive_1980 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_82
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
               ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254
                  ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1644 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))))))
-- Relation.Binary.Lattice.BooleanAlgebra._.setoid
d_setoid_1982 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
d_setoid_1982 :: T_Level_18
-> T_Level_18 -> T_Level_18 -> T_BooleanAlgebra_1878 -> T_Setoid_44
d_setoid_1982 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3 = T_BooleanAlgebra_1878 -> T_Setoid_44
du_setoid_1982 T_BooleanAlgebra_1878
v3
du_setoid_1982 ::
  T_BooleanAlgebra_1878 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Setoid_44
du_setoid_1982 :: T_BooleanAlgebra_1878 -> T_Setoid_44
du_setoid_1982 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0) in
    AgdaAny -> T_Setoid_44
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_Lattice_898 -> T_Setoid_44) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_Lattice_898 -> T_Setoid_44
du_setoid_984 ((T_BoundedLattice_1324 -> T_Lattice_898) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BoundedLattice_1324 -> T_Lattice_898
du_lattice_1432 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v2))))
-- Relation.Binary.Lattice.BooleanAlgebra._.supremum
d_supremum_1984 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_supremum_1984 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> AgdaAny
-> AgdaAny
-> T_Σ_14
d_supremum_1984 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3 = T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> T_Σ_14
du_supremum_1984 T_BooleanAlgebra_1878
v3
du_supremum_1984 ::
  T_BooleanAlgebra_1878 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_supremum_1984 :: T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> T_Σ_14
du_supremum_1984 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      ((T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_810 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_836
         ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254
            ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1644 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))))
-- Relation.Binary.Lattice.BooleanAlgebra._.trans
d_trans_1986 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_1986 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_1986 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3 = T_BooleanAlgebra_1878
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1986 T_BooleanAlgebra_1878
v3
du_trans_1986 ::
  T_BooleanAlgebra_1878 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1986 :: T_BooleanAlgebra_1878
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_1986 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_84
         ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
            ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
               ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254
                  ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496 ((T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1644 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))))))
-- Relation.Binary.Lattice.BooleanAlgebra._.transpose-⇨
d_transpose'45''8680'_1988 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_transpose'45''8680'_1988 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_transpose'45''8680'_1988 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3
  = T_BooleanAlgebra_1878
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8680'_1988 T_BooleanAlgebra_1878
v3
du_transpose'45''8680'_1988 ::
  T_BooleanAlgebra_1878 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8680'_1988 :: T_BooleanAlgebra_1878
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8680'_1988 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsHeytingAlgebra_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsHeytingAlgebra_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8680'_1506 ((T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1644 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Relation.Binary.Lattice.BooleanAlgebra._.transpose-∧
d_transpose'45''8743'_1990 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_transpose'45''8743'_1990 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_transpose'45''8743'_1990 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3
  = T_BooleanAlgebra_1878
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8743'_1990 T_BooleanAlgebra_1878
v3
du_transpose'45''8743'_1990 ::
  T_BooleanAlgebra_1878 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8743'_1990 :: T_BooleanAlgebra_1878
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8743'_1990 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsHeytingAlgebra_1468
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsHeytingAlgebra_1468
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8743'_1522 ((T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1644 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1)))
-- Relation.Binary.Lattice.BooleanAlgebra._.x∧y≤x
d_x'8743'y'8804'x_1992 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'x_1992 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'x_1992 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3 = T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_1992 T_BooleanAlgebra_1878
v3
du_x'8743'y'8804'x_1992 ::
  T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_1992 :: T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_1992 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsBoundedLattice_1226
v3 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (AgdaAny -> T_BoundedLattice_1324
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsLattice_810
v4 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_466 ((T_IsLattice_810 -> T_IsMeetSemilattice_438) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v4))))))
-- Relation.Binary.Lattice.BooleanAlgebra._.x∧y≤y
d_x'8743'y'8804'y_1994 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'y_1994 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'y_1994 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3 = T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_1994 T_BooleanAlgebra_1878
v3
du_x'8743'y'8804'y_1994 ::
  T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_1994 :: T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_1994 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsBoundedLattice_1226
v3 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (AgdaAny -> T_BoundedLattice_1324
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsLattice_810
v4 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMeetSemilattice_438 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_478 ((T_IsLattice_810 -> T_IsMeetSemilattice_438) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v4))))))
-- Relation.Binary.Lattice.BooleanAlgebra._.x≤x∨y
d_x'8804'x'8744'y_1996 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8804'x'8744'y_1996 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8804'x'8744'y_1996 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3 = T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_1996 T_BooleanAlgebra_1878
v3
du_x'8804'x'8744'y_1996 ::
  T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_1996 :: T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_1996 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsBoundedLattice_1226
v3 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (AgdaAny -> T_BoundedLattice_1324
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsLattice_810
v4 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_96 ((T_IsLattice_810 -> T_IsJoinSemilattice_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v4))))))
-- Relation.Binary.Lattice.BooleanAlgebra._.y≤x∨y
d_y'8804'x'8744'y_1998 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny
d_y'8804'x'8744'y_1998 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_y'8804'x'8744'y_1998 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3 = T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_1998 T_BooleanAlgebra_1878
v3
du_y'8804'x'8744'y_1998 ::
  T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_1998 :: T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_1998 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsBoundedLattice_1226
v3 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (AgdaAny -> T_BoundedLattice_1324
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsLattice_810
v4 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsJoinSemilattice_68 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_108 ((T_IsLattice_810 -> T_IsJoinSemilattice_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v4))))))
-- Relation.Binary.Lattice.BooleanAlgebra._.∧-greatest
d_'8743''45'greatest_2000 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'greatest_2000 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'greatest_2000 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3
  = T_BooleanAlgebra_1878
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_2000 T_BooleanAlgebra_1878
v3
du_'8743''45'greatest_2000 ::
  T_BooleanAlgebra_1878 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_2000 :: T_BooleanAlgebra_1878
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_2000 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsBoundedLattice_1226
v3 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (AgdaAny -> T_BoundedLattice_1324
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsLattice_810
v4 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsMeetSemilattice_438
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsMeetSemilattice_438
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_492
                  ((T_IsLattice_810 -> T_IsMeetSemilattice_438) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsMeetSemilattice_438
du_isMeetSemilattice_842 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v4))))))
-- Relation.Binary.Lattice.BooleanAlgebra._.∨-least
d_'8744''45'least_2002 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'least_2002 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'least_2002 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3 = T_BooleanAlgebra_1878
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_2002 T_BooleanAlgebra_1878
v3
du_'8744''45'least_2002 ::
  T_BooleanAlgebra_1878 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_2002 :: T_BooleanAlgebra_1878
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_2002 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsBoundedLattice_1226
v3 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (AgdaAny -> T_BoundedLattice_1324
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsLattice_810
v4 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsJoinSemilattice_68
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsJoinSemilattice_68
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_122 ((T_IsLattice_810 -> T_IsJoinSemilattice_68) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810 -> T_IsJoinSemilattice_68
du_isJoinSemilattice_840 (T_IsLattice_810 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_810
v4))))))
-- Relation.Binary.Lattice.BooleanAlgebra._.∼-resp-≈
d_'8764''45'resp'45''8776'_2004 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_2004 :: T_Level_18
-> T_Level_18 -> T_Level_18 -> T_BooleanAlgebra_1878 -> T_Σ_14
d_'8764''45'resp'45''8776'_2004 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3
  = T_BooleanAlgebra_1878 -> T_Σ_14
du_'8764''45'resp'45''8776'_2004 T_BooleanAlgebra_1878
v3
du_'8764''45'resp'45''8776'_2004 ::
  T_BooleanAlgebra_1878 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_2004 :: T_BooleanAlgebra_1878 -> T_Σ_14
du_'8764''45'resp'45''8776'_2004 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsBoundedLattice_1226
v3 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (AgdaAny -> T_BoundedLattice_1324
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsLattice_810
v4 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_162
v5 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsPreorder_70 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPreorder_70 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_112
                     ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                        (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v5)))))))
-- Relation.Binary.Lattice.BooleanAlgebra._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_2006 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_2006 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_2006 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3
  = T_BooleanAlgebra_1878
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_2006 T_BooleanAlgebra_1878
v3
du_'8764''45'resp'691''45''8776'_2006 ::
  T_BooleanAlgebra_1878 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_2006 :: T_BooleanAlgebra_1878
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_2006 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsBoundedLattice_1226
v3 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (AgdaAny -> T_BoundedLattice_1324
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsLattice_810
v4 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_162
v5 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_106
                     ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                        (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v5)))))))
-- Relation.Binary.Lattice.BooleanAlgebra._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_2008 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_2008 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_2008 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3
  = T_BooleanAlgebra_1878
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_2008 T_BooleanAlgebra_1878
v3
du_'8764''45'resp'737''45''8776'_2008 ::
  T_BooleanAlgebra_1878 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_2008 :: T_BooleanAlgebra_1878
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_2008 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsBoundedLattice_1226
v3 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (AgdaAny -> T_BoundedLattice_1324
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsLattice_810
v4 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_162
v5 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsPreorder_70
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPreorder_70
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_100
                     ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                        (T_IsPartialOrder_162 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_162
v5)))))))
-- Relation.Binary.Lattice.BooleanAlgebra._.Eq.isPartialEquivalence
d_isPartialEquivalence_2012 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_2012 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_2012 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3
  = T_BooleanAlgebra_1878 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2012 T_BooleanAlgebra_1878
v3
du_isPartialEquivalence_2012 ::
  T_BooleanAlgebra_1878 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_2012 :: T_BooleanAlgebra_1878 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_2012 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsBoundedLattice_1226
v3 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (AgdaAny -> T_BoundedLattice_1324
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsLattice_810
v4 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_162
v5 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPreorder_70
v6
                         = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                             (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
v5) 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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                           (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v6))))))))
-- Relation.Binary.Lattice.BooleanAlgebra._.Eq.refl
d_refl_2014 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny
d_refl_2014 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> AgdaAny
-> AgdaAny
d_refl_2014 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3 = T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny
du_refl_2014 T_BooleanAlgebra_1878
v3
du_refl_2014 :: T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny
du_refl_2014 :: T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny
du_refl_2014 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
            ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
               ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
                  ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254
                     ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496
                        ((T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1644 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1))))))))
-- Relation.Binary.Lattice.BooleanAlgebra._.Eq.reflexive
d_reflexive_2016 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_2016 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_2016 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3 = T_BooleanAlgebra_1878
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2016 T_BooleanAlgebra_1878
v3
du_reflexive_2016 ::
  T_BooleanAlgebra_1878 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_2016 :: T_BooleanAlgebra_1878
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_2016 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: t
v2 = (T_HeytingAlgebra_1602 -> T_BoundedLattice_1324) -> AgdaAny -> t
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_BoundedLattice_1324
du_boundedLattice_1646 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsBoundedLattice_1226
v3 = T_BoundedLattice_1324 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1362 (AgdaAny -> T_BoundedLattice_1324
forall a b. a -> b
coe AgdaAny
forall a. a
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsLattice_810
v4 = T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254 (T_IsBoundedLattice_1226 -> T_IsBoundedLattice_1226
forall a b. a -> b
coe T_IsBoundedLattice_1226
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPartialOrder_162
v5 = T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834 (T_IsLattice_810 -> T_IsLattice_810
forall a b. a -> b
coe T_IsLattice_810
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (let v6 :: T_IsPreorder_70
v6
                         = T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
                             (T_IsPartialOrder_162 -> T_IsPartialOrder_162
forall a b. a -> b
coe T_IsPartialOrder_162
v5) in
                   (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                     (\ AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 ->
                        (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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                             T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
                             (T_IsPreorder_70 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_70
v6))
                          AgdaAny
v7))))))
-- Relation.Binary.Lattice.BooleanAlgebra._.Eq.sym
d_sym_2018 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_2018 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_sym_2018 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3 = T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2018 T_BooleanAlgebra_1878
v3
du_sym_2018 ::
  T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2018 :: T_BooleanAlgebra_1878 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_sym_2018 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
            ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
               ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
                  ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254
                     ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496
                        ((T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1644 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1))))))))
-- Relation.Binary.Lattice.BooleanAlgebra._.Eq.trans
d_trans_2020 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  T_BooleanAlgebra_1878 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_2020 :: T_Level_18
-> T_Level_18
-> T_Level_18
-> T_BooleanAlgebra_1878
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_trans_2020 ~T_Level_18
v0 ~T_Level_18
v1 ~T_Level_18
v2 T_BooleanAlgebra_1878
v3 = T_BooleanAlgebra_1878
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2020 T_BooleanAlgebra_1878
v3
du_trans_2020 ::
  T_BooleanAlgebra_1878 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2020 :: T_BooleanAlgebra_1878
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_trans_2020 T_BooleanAlgebra_1878
v0
  = let v1 :: t
v1 = (T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602) -> AgdaAny -> t
forall a b. a -> b
coe T_BooleanAlgebra_1878 -> T_HeytingAlgebra_1602
du_heytingAlgebra_1926 (T_BooleanAlgebra_1878 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_1878
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_IsPreorder_70 -> T_IsEquivalence_26) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_70 -> T_IsEquivalence_26
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_80
            ((T_IsPartialOrder_162 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_162 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_170
               ((T_IsLattice_810 -> T_IsPartialOrder_162) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLattice_810 -> T_IsPartialOrder_162
d_isPartialOrder_834
                  ((T_IsBoundedLattice_1226 -> T_IsLattice_810) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsBoundedLattice_1226 -> T_IsLattice_810
d_isLattice_1254
                     ((T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsHeytingAlgebra_1468 -> T_IsBoundedLattice_1226
d_isBoundedLattice_1496
                        ((T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_HeytingAlgebra_1602 -> T_IsHeytingAlgebra_1468
d_isHeytingAlgebra_1644 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
forall a. a
v1))))))))