{-# 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.Structures where

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

-- Relation.Binary.Lattice.Structures.IsJoinSemilattice
d_IsJoinSemilattice_22 :: p -> p -> p -> p -> p -> p -> p -> ()
d_IsJoinSemilattice_22 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsJoinSemilattice_22
  = C_IsJoinSemilattice'46'constructor_527 MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_174
                                           (AgdaAny ->
                                            AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14)
-- Relation.Binary.Lattice.Structures.IsJoinSemilattice.isPartialOrder
d_isPartialOrder_30 ::
  T_IsJoinSemilattice_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_174
d_isPartialOrder_30 :: T_IsJoinSemilattice_22 -> T_IsPartialOrder_174
d_isPartialOrder_30 T_IsJoinSemilattice_22
v0
  = case T_IsJoinSemilattice_22 -> T_IsJoinSemilattice_22
forall a b. a -> b
coe T_IsJoinSemilattice_22
v0 of
      C_IsJoinSemilattice'46'constructor_527 T_IsPartialOrder_174
v1 AgdaAny -> AgdaAny -> T_Σ_14
v2 -> T_IsPartialOrder_174 -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsPartialOrder_174
v1
      T_IsJoinSemilattice_22
_ -> T_IsPartialOrder_174
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.Structures.IsJoinSemilattice.supremum
d_supremum_32 ::
  T_IsJoinSemilattice_22 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_supremum_32 :: T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_32 T_IsJoinSemilattice_22
v0
  = case T_IsJoinSemilattice_22 -> T_IsJoinSemilattice_22
forall a b. a -> b
coe T_IsJoinSemilattice_22
v0 of
      C_IsJoinSemilattice'46'constructor_527 T_IsPartialOrder_174
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_22
_ -> AgdaAny -> AgdaAny -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.Structures.IsJoinSemilattice.x≤x∨y
d_x'8804'x'8744'y_38 ::
  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_22 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8804'x'8744'y_38 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsJoinSemilattice_22
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8804'x'8744'y_38 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsJoinSemilattice_22
v7 AgdaAny
v8 AgdaAny
v9
  = T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_38 T_IsJoinSemilattice_22
v7 AgdaAny
v8 AgdaAny
v9
du_x'8804'x'8744'y_38 ::
  T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_38 :: T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_38 T_IsJoinSemilattice_22
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_22 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_32 T_IsJoinSemilattice_22
v0 AgdaAny
v1 AgdaAny
v2)
-- Relation.Binary.Lattice.Structures.IsJoinSemilattice.y≤x∨y
d_y'8804'x'8744'y_50 ::
  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_22 -> AgdaAny -> AgdaAny -> AgdaAny
d_y'8804'x'8744'y_50 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsJoinSemilattice_22
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_y'8804'x'8744'y_50 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsJoinSemilattice_22
v7 AgdaAny
v8 AgdaAny
v9
  = T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_50 T_IsJoinSemilattice_22
v7 AgdaAny
v8 AgdaAny
v9
du_y'8804'x'8744'y_50 ::
  T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_50 :: T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_50 T_IsJoinSemilattice_22
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_22 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_32 T_IsJoinSemilattice_22
v0 AgdaAny
v1 AgdaAny
v2))
-- Relation.Binary.Lattice.Structures.IsJoinSemilattice.∨-least
d_'8744''45'least_64 ::
  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_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'least_64 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsJoinSemilattice_22
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'least_64 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsJoinSemilattice_22
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
  = T_IsJoinSemilattice_22
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_64 T_IsJoinSemilattice_22
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
du_'8744''45'least_64 ::
  T_IsJoinSemilattice_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_64 :: T_IsJoinSemilattice_22
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_64 T_IsJoinSemilattice_22
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_22 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_32 T_IsJoinSemilattice_22
v0 AgdaAny
v1 AgdaAny
v2))
      AgdaAny
v3
-- Relation.Binary.Lattice.Structures.IsJoinSemilattice._.antisym
d_antisym_76 ::
  T_IsJoinSemilattice_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_76 :: T_IsJoinSemilattice_22
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_76 T_IsJoinSemilattice_22
v0
  = (T_IsPartialOrder_174
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_174
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_184
      ((T_IsJoinSemilattice_22 -> T_IsPartialOrder_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> T_IsPartialOrder_174
d_isPartialOrder_30 (T_IsJoinSemilattice_22 -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22
v0))
-- Relation.Binary.Lattice.Structures.IsJoinSemilattice._.isEquivalence
d_isEquivalence_78 ::
  T_IsJoinSemilattice_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_78 :: T_IsJoinSemilattice_22 -> T_IsEquivalence_26
d_isEquivalence_78 T_IsJoinSemilattice_22
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsJoinSemilattice_22 -> T_IsPartialOrder_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> T_IsPartialOrder_174
d_isPartialOrder_30 (T_IsJoinSemilattice_22 -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22
v0)))
-- Relation.Binary.Lattice.Structures.IsJoinSemilattice._.isPreorder
d_isPreorder_80 ::
  T_IsJoinSemilattice_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_80 :: T_IsJoinSemilattice_22 -> T_IsPreorder_70
d_isPreorder_80 T_IsJoinSemilattice_22
v0
  = (T_IsPartialOrder_174 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
      ((T_IsJoinSemilattice_22 -> T_IsPartialOrder_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> T_IsPartialOrder_174
d_isPartialOrder_30 (T_IsJoinSemilattice_22 -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22
v0))
-- Relation.Binary.Lattice.Structures.IsJoinSemilattice._.refl
d_refl_82 ::
  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_22 -> AgdaAny -> AgdaAny
d_refl_82 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsJoinSemilattice_22
-> AgdaAny
-> AgdaAny
d_refl_82 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsJoinSemilattice_22
v7 = T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny
du_refl_82 T_IsJoinSemilattice_22
v7
du_refl_82 :: T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny
du_refl_82 :: T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny
du_refl_82 T_IsJoinSemilattice_22
v0
  = let v1 :: T_IsPartialOrder_174
v1 = T_IsJoinSemilattice_22 -> T_IsPartialOrder_174
d_isPartialOrder_30 (T_IsJoinSemilattice_22 -> T_IsJoinSemilattice_22
forall a b. a -> b
coe T_IsJoinSemilattice_22
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182 (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v1)))
-- Relation.Binary.Lattice.Structures.IsJoinSemilattice._.reflexive
d_reflexive_84 ::
  T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_84 :: T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_84 T_IsJoinSemilattice_22
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsJoinSemilattice_22 -> T_IsPartialOrder_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> T_IsPartialOrder_174
d_isPartialOrder_30 (T_IsJoinSemilattice_22 -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22
v0)))
-- Relation.Binary.Lattice.Structures.IsJoinSemilattice._.trans
d_trans_86 ::
  T_IsJoinSemilattice_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_86 :: T_IsJoinSemilattice_22
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_86 T_IsJoinSemilattice_22
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsJoinSemilattice_22 -> T_IsPartialOrder_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> T_IsPartialOrder_174
d_isPartialOrder_30 (T_IsJoinSemilattice_22 -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22
v0)))
-- Relation.Binary.Lattice.Structures.IsJoinSemilattice._.∼-resp-≈
d_'8764''45'resp'45''8776'_88 ::
  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_22 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_88 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsJoinSemilattice_22
-> T_Σ_14
d_'8764''45'resp'45''8776'_88 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsJoinSemilattice_22
v7
  = T_IsJoinSemilattice_22 -> T_Σ_14
du_'8764''45'resp'45''8776'_88 T_IsJoinSemilattice_22
v7
du_'8764''45'resp'45''8776'_88 ::
  T_IsJoinSemilattice_22 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_88 :: T_IsJoinSemilattice_22 -> T_Σ_14
du_'8764''45'resp'45''8776'_88 T_IsJoinSemilattice_22
v0
  = let v1 :: T_IsPartialOrder_174
v1 = T_IsJoinSemilattice_22 -> T_IsPartialOrder_174
d_isPartialOrder_30 (T_IsJoinSemilattice_22 -> T_IsJoinSemilattice_22
forall a b. a -> b
coe T_IsJoinSemilattice_22
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'_118
         ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182 (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v1)))
-- Relation.Binary.Lattice.Structures.IsJoinSemilattice._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_90 ::
  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_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_90 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsJoinSemilattice_22
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_90 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsJoinSemilattice_22
v7
  = T_IsJoinSemilattice_22
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_90 T_IsJoinSemilattice_22
v7
du_'8764''45'resp'691''45''8776'_90 ::
  T_IsJoinSemilattice_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_90 :: T_IsJoinSemilattice_22
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_90 T_IsJoinSemilattice_22
v0
  = let v1 :: T_IsPartialOrder_174
v1 = T_IsJoinSemilattice_22 -> T_IsPartialOrder_174
d_isPartialOrder_30 (T_IsJoinSemilattice_22 -> T_IsJoinSemilattice_22
forall a b. a -> b
coe T_IsJoinSemilattice_22
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'_116
         ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182 (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v1)))
-- Relation.Binary.Lattice.Structures.IsJoinSemilattice._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_92 ::
  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_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_92 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsJoinSemilattice_22
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_92 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsJoinSemilattice_22
v7
  = T_IsJoinSemilattice_22
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_92 T_IsJoinSemilattice_22
v7
du_'8764''45'resp'737''45''8776'_92 ::
  T_IsJoinSemilattice_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_92 :: T_IsJoinSemilattice_22
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_92 T_IsJoinSemilattice_22
v0
  = let v1 :: T_IsPartialOrder_174
v1 = T_IsJoinSemilattice_22 -> T_IsPartialOrder_174
d_isPartialOrder_30 (T_IsJoinSemilattice_22 -> T_IsJoinSemilattice_22
forall a b. a -> b
coe T_IsJoinSemilattice_22
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'_114
         ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182 (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v1)))
-- Relation.Binary.Lattice.Structures.IsJoinSemilattice._.≲-resp-≈
d_'8818''45'resp'45''8776'_94 ::
  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_22 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8818''45'resp'45''8776'_94 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsJoinSemilattice_22
-> T_Σ_14
d_'8818''45'resp'45''8776'_94 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsJoinSemilattice_22
v7
  = T_IsJoinSemilattice_22 -> T_Σ_14
du_'8818''45'resp'45''8776'_94 T_IsJoinSemilattice_22
v7
du_'8818''45'resp'45''8776'_94 ::
  T_IsJoinSemilattice_22 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8818''45'resp'45''8776'_94 :: T_IsJoinSemilattice_22 -> T_Σ_14
du_'8818''45'resp'45''8776'_94 T_IsJoinSemilattice_22
v0
  = let v1 :: T_IsPartialOrder_174
v1 = T_IsJoinSemilattice_22 -> T_IsPartialOrder_174
d_isPartialOrder_30 (T_IsJoinSemilattice_22 -> T_IsJoinSemilattice_22
forall a b. a -> b
coe T_IsJoinSemilattice_22
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_'8818''45'resp'45''8776'_112
         ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182 (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v1)))
-- Relation.Binary.Lattice.Structures.IsJoinSemilattice._.≲-respʳ-≈
d_'8818''45'resp'691''45''8776'_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_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'691''45''8776'_96 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsJoinSemilattice_22
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'691''45''8776'_96 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsJoinSemilattice_22
v7
  = T_IsJoinSemilattice_22
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_96 T_IsJoinSemilattice_22
v7
du_'8818''45'resp'691''45''8776'_96 ::
  T_IsJoinSemilattice_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_96 :: T_IsJoinSemilattice_22
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_96 T_IsJoinSemilattice_22
v0
  = let v1 :: T_IsPartialOrder_174
v1 = T_IsJoinSemilattice_22 -> T_IsPartialOrder_174
d_isPartialOrder_30 (T_IsJoinSemilattice_22 -> T_IsJoinSemilattice_22
forall a b. a -> b
coe T_IsJoinSemilattice_22
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_'8818''45'resp'691''45''8776'_106
         ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182 (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v1)))
-- Relation.Binary.Lattice.Structures.IsJoinSemilattice._.≲-respˡ-≈
d_'8818''45'resp'737''45''8776'_98 ::
  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_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'737''45''8776'_98 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsJoinSemilattice_22
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'737''45''8776'_98 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsJoinSemilattice_22
v7
  = T_IsJoinSemilattice_22
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_98 T_IsJoinSemilattice_22
v7
du_'8818''45'resp'737''45''8776'_98 ::
  T_IsJoinSemilattice_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_98 :: T_IsJoinSemilattice_22
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_98 T_IsJoinSemilattice_22
v0
  = let v1 :: T_IsPartialOrder_174
v1 = T_IsJoinSemilattice_22 -> T_IsPartialOrder_174
d_isPartialOrder_30 (T_IsJoinSemilattice_22 -> T_IsJoinSemilattice_22
forall a b. a -> b
coe T_IsJoinSemilattice_22
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_'8818''45'resp'737''45''8776'_100
         ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182 (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v1)))
-- Relation.Binary.Lattice.Structures.IsJoinSemilattice._.Eq.isPartialEquivalence
d_isPartialEquivalence_102 ::
  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_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_102 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsJoinSemilattice_22
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_102 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsJoinSemilattice_22
v7
  = T_IsJoinSemilattice_22 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_102 T_IsJoinSemilattice_22
v7
du_isPartialEquivalence_102 ::
  T_IsJoinSemilattice_22 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_102 :: T_IsJoinSemilattice_22 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_102 T_IsJoinSemilattice_22
v0
  = let v1 :: T_IsPartialOrder_174
v1 = T_IsJoinSemilattice_22 -> T_IsPartialOrder_174
d_isPartialOrder_30 (T_IsJoinSemilattice_22 -> T_IsJoinSemilattice_22
forall a b. a -> b
coe T_IsJoinSemilattice_22
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPreorder_70
v2
             = T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                 (T_IsPartialOrder_174 -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsPartialOrder_174
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.Structures.IsJoinSemilattice._.Eq.refl
d_refl_104 :: T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny
d_refl_104 :: T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny
d_refl_104 T_IsJoinSemilattice_22
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsJoinSemilattice_22 -> T_IsPartialOrder_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> T_IsPartialOrder_174
d_isPartialOrder_30 (T_IsJoinSemilattice_22 -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22
v0))))
-- Relation.Binary.Lattice.Structures.IsJoinSemilattice._.Eq.reflexive
d_reflexive_106 ::
  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_22 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_106 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsJoinSemilattice_22
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_106 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsJoinSemilattice_22
v7
  = T_IsJoinSemilattice_22
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_106 T_IsJoinSemilattice_22
v7
du_reflexive_106 ::
  T_IsJoinSemilattice_22 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_106 :: T_IsJoinSemilattice_22
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_106 T_IsJoinSemilattice_22
v0
  = let v1 :: T_IsPartialOrder_174
v1 = T_IsJoinSemilattice_22 -> T_IsPartialOrder_174
d_isPartialOrder_30 (T_IsJoinSemilattice_22 -> T_IsJoinSemilattice_22
forall a b. a -> b
coe T_IsJoinSemilattice_22
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPreorder_70
v2
             = T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                 (T_IsPartialOrder_174 -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsPartialOrder_174
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.Structures.IsJoinSemilattice._.Eq.sym
d_sym_108 ::
  T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_108 :: T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_108 T_IsJoinSemilattice_22
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsJoinSemilattice_22 -> T_IsPartialOrder_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> T_IsPartialOrder_174
d_isPartialOrder_30 (T_IsJoinSemilattice_22 -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22
v0))))
-- Relation.Binary.Lattice.Structures.IsJoinSemilattice._.Eq.trans
d_trans_110 ::
  T_IsJoinSemilattice_22 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_110 :: T_IsJoinSemilattice_22
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_110 T_IsJoinSemilattice_22
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsJoinSemilattice_22 -> T_IsPartialOrder_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> T_IsPartialOrder_174
d_isPartialOrder_30 (T_IsJoinSemilattice_22 -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22
v0))))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice
d_IsBoundedJoinSemilattice_116 :: p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsBoundedJoinSemilattice_116 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 = ()
data T_IsBoundedJoinSemilattice_116
  = C_IsBoundedJoinSemilattice'46'constructor_5215 T_IsJoinSemilattice_22
                                                   (AgdaAny -> AgdaAny)
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice.isJoinSemilattice
d_isJoinSemilattice_126 ::
  T_IsBoundedJoinSemilattice_116 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_126 :: T_IsBoundedJoinSemilattice_116 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_126 T_IsBoundedJoinSemilattice_116
v0
  = case T_IsBoundedJoinSemilattice_116 -> T_IsBoundedJoinSemilattice_116
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_116
v0 of
      C_IsBoundedJoinSemilattice'46'constructor_5215 T_IsJoinSemilattice_22
v1 AgdaAny -> AgdaAny
v2 -> T_IsJoinSemilattice_22 -> T_IsJoinSemilattice_22
forall a b. a -> b
coe T_IsJoinSemilattice_22
v1
      T_IsBoundedJoinSemilattice_116
_ -> T_IsJoinSemilattice_22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice.minimum
d_minimum_128 ::
  T_IsBoundedJoinSemilattice_116 -> AgdaAny -> AgdaAny
d_minimum_128 :: T_IsBoundedJoinSemilattice_116 -> AgdaAny -> AgdaAny
d_minimum_128 T_IsBoundedJoinSemilattice_116
v0
  = case T_IsBoundedJoinSemilattice_116 -> T_IsBoundedJoinSemilattice_116
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_116
v0 of
      C_IsBoundedJoinSemilattice'46'constructor_5215 T_IsJoinSemilattice_22
v1 AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_IsBoundedJoinSemilattice_116
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.antisym
d_antisym_132 ::
  T_IsBoundedJoinSemilattice_116 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_132 :: T_IsBoundedJoinSemilattice_116
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_132 T_IsBoundedJoinSemilattice_116
v0
  = (T_IsPartialOrder_174
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_174
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_184
      ((T_IsJoinSemilattice_22 -> T_IsPartialOrder_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> T_IsPartialOrder_174
d_isPartialOrder_30 ((T_IsBoundedJoinSemilattice_116 -> T_IsJoinSemilattice_22)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_116 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_126 (T_IsBoundedJoinSemilattice_116 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_116
v0)))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.isEquivalence
d_isEquivalence_134 ::
  T_IsBoundedJoinSemilattice_116 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_134 :: T_IsBoundedJoinSemilattice_116 -> T_IsEquivalence_26
d_isEquivalence_134 T_IsBoundedJoinSemilattice_116
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsJoinSemilattice_22 -> T_IsPartialOrder_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> T_IsPartialOrder_174
d_isPartialOrder_30 ((T_IsBoundedJoinSemilattice_116 -> T_IsJoinSemilattice_22)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_116 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_126 (T_IsBoundedJoinSemilattice_116 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_116
v0))))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.isPartialOrder
d_isPartialOrder_136 ::
  T_IsBoundedJoinSemilattice_116 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_174
d_isPartialOrder_136 :: T_IsBoundedJoinSemilattice_116 -> T_IsPartialOrder_174
d_isPartialOrder_136 T_IsBoundedJoinSemilattice_116
v0
  = (T_IsJoinSemilattice_22 -> T_IsPartialOrder_174)
-> AgdaAny -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> T_IsPartialOrder_174
d_isPartialOrder_30 ((T_IsBoundedJoinSemilattice_116 -> T_IsJoinSemilattice_22)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_116 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_126 (T_IsBoundedJoinSemilattice_116 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_116
v0))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.isPreorder
d_isPreorder_138 ::
  T_IsBoundedJoinSemilattice_116 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_138 :: T_IsBoundedJoinSemilattice_116 -> T_IsPreorder_70
d_isPreorder_138 T_IsBoundedJoinSemilattice_116
v0
  = (T_IsPartialOrder_174 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
      ((T_IsJoinSemilattice_22 -> T_IsPartialOrder_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> T_IsPartialOrder_174
d_isPartialOrder_30 ((T_IsBoundedJoinSemilattice_116 -> T_IsJoinSemilattice_22)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_116 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_126 (T_IsBoundedJoinSemilattice_116 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_116
v0)))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.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) ->
  AgdaAny -> T_IsBoundedJoinSemilattice_116 -> AgdaAny -> AgdaAny
d_refl_140 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedJoinSemilattice_116
-> AgdaAny
-> AgdaAny
d_refl_140 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedJoinSemilattice_116
v8 = T_IsBoundedJoinSemilattice_116 -> AgdaAny -> AgdaAny
du_refl_140 T_IsBoundedJoinSemilattice_116
v8
du_refl_140 :: T_IsBoundedJoinSemilattice_116 -> AgdaAny -> AgdaAny
du_refl_140 :: T_IsBoundedJoinSemilattice_116 -> AgdaAny -> AgdaAny
du_refl_140 T_IsBoundedJoinSemilattice_116
v0
  = let v1 :: T_IsJoinSemilattice_22
v1 = T_IsBoundedJoinSemilattice_116 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_126 (T_IsBoundedJoinSemilattice_116 -> T_IsBoundedJoinSemilattice_116
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_116
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsJoinSemilattice_22 -> T_IsPartialOrder_174
d_isPartialOrder_30 (T_IsJoinSemilattice_22 -> T_IsJoinSemilattice_22
forall a b. a -> b
coe T_IsJoinSemilattice_22
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.reflexive
d_reflexive_142 ::
  T_IsBoundedJoinSemilattice_116 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_142 :: T_IsBoundedJoinSemilattice_116
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_142 T_IsBoundedJoinSemilattice_116
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsJoinSemilattice_22 -> T_IsPartialOrder_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> T_IsPartialOrder_174
d_isPartialOrder_30 ((T_IsBoundedJoinSemilattice_116 -> T_IsJoinSemilattice_22)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_116 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_126 (T_IsBoundedJoinSemilattice_116 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_116
v0))))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.supremum
d_supremum_144 ::
  T_IsBoundedJoinSemilattice_116 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_supremum_144 :: T_IsBoundedJoinSemilattice_116 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_144 T_IsBoundedJoinSemilattice_116
v0
  = (T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_32 ((T_IsBoundedJoinSemilattice_116 -> T_IsJoinSemilattice_22)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_116 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_126 (T_IsBoundedJoinSemilattice_116 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_116
v0))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.trans
d_trans_146 ::
  T_IsBoundedJoinSemilattice_116 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_146 :: T_IsBoundedJoinSemilattice_116
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_146 T_IsBoundedJoinSemilattice_116
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsJoinSemilattice_22 -> T_IsPartialOrder_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> T_IsPartialOrder_174
d_isPartialOrder_30 ((T_IsBoundedJoinSemilattice_116 -> T_IsJoinSemilattice_22)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_116 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_126 (T_IsBoundedJoinSemilattice_116 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_116
v0))))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.x≤x∨y
d_x'8804'x'8744'y_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) ->
  AgdaAny ->
  T_IsBoundedJoinSemilattice_116 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8804'x'8744'y_148 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedJoinSemilattice_116
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8804'x'8744'y_148 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedJoinSemilattice_116
v8
  = T_IsBoundedJoinSemilattice_116 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_148 T_IsBoundedJoinSemilattice_116
v8
du_x'8804'x'8744'y_148 ::
  T_IsBoundedJoinSemilattice_116 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_148 :: T_IsBoundedJoinSemilattice_116 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_148 T_IsBoundedJoinSemilattice_116
v0
  = (T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_38 ((T_IsBoundedJoinSemilattice_116 -> T_IsJoinSemilattice_22)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_116 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_126 (T_IsBoundedJoinSemilattice_116 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_116
v0))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.y≤x∨y
d_y'8804'x'8744'y_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) ->
  AgdaAny ->
  T_IsBoundedJoinSemilattice_116 -> AgdaAny -> AgdaAny -> AgdaAny
d_y'8804'x'8744'y_150 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedJoinSemilattice_116
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_y'8804'x'8744'y_150 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedJoinSemilattice_116
v8
  = T_IsBoundedJoinSemilattice_116 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_150 T_IsBoundedJoinSemilattice_116
v8
du_y'8804'x'8744'y_150 ::
  T_IsBoundedJoinSemilattice_116 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_150 :: T_IsBoundedJoinSemilattice_116 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_150 T_IsBoundedJoinSemilattice_116
v0
  = (T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_50 ((T_IsBoundedJoinSemilattice_116 -> T_IsJoinSemilattice_22)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_116 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_126 (T_IsBoundedJoinSemilattice_116 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_116
v0))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.∨-least
d_'8744''45'least_152 ::
  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_116 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'least_152 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedJoinSemilattice_116
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'least_152 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedJoinSemilattice_116
v8
  = T_IsBoundedJoinSemilattice_116
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_152 T_IsBoundedJoinSemilattice_116
v8
du_'8744''45'least_152 ::
  T_IsBoundedJoinSemilattice_116 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_152 :: T_IsBoundedJoinSemilattice_116
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_152 T_IsBoundedJoinSemilattice_116
v0
  = (T_IsJoinSemilattice_22
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_64 ((T_IsBoundedJoinSemilattice_116 -> T_IsJoinSemilattice_22)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_116 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_126 (T_IsBoundedJoinSemilattice_116 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_116
v0))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.∼-resp-≈
d_'8764''45'resp'45''8776'_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) ->
  AgdaAny ->
  T_IsBoundedJoinSemilattice_116 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_154 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedJoinSemilattice_116
-> T_Σ_14
d_'8764''45'resp'45''8776'_154 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedJoinSemilattice_116
v8
  = T_IsBoundedJoinSemilattice_116 -> T_Σ_14
du_'8764''45'resp'45''8776'_154 T_IsBoundedJoinSemilattice_116
v8
du_'8764''45'resp'45''8776'_154 ::
  T_IsBoundedJoinSemilattice_116 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_154 :: T_IsBoundedJoinSemilattice_116 -> T_Σ_14
du_'8764''45'resp'45''8776'_154 T_IsBoundedJoinSemilattice_116
v0
  = let v1 :: T_IsJoinSemilattice_22
v1 = T_IsBoundedJoinSemilattice_116 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_126 (T_IsBoundedJoinSemilattice_116 -> T_IsBoundedJoinSemilattice_116
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_116
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsJoinSemilattice_22 -> T_IsPartialOrder_174
d_isPartialOrder_30 (T_IsJoinSemilattice_22 -> T_IsJoinSemilattice_22
forall a b. a -> b
coe T_IsJoinSemilattice_22
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'_118
            ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_156 ::
  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_116 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_156 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedJoinSemilattice_116
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_156 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7
                                    T_IsBoundedJoinSemilattice_116
v8
  = T_IsBoundedJoinSemilattice_116
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_156 T_IsBoundedJoinSemilattice_116
v8
du_'8764''45'resp'691''45''8776'_156 ::
  T_IsBoundedJoinSemilattice_116 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_156 :: T_IsBoundedJoinSemilattice_116
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_156 T_IsBoundedJoinSemilattice_116
v0
  = let v1 :: T_IsJoinSemilattice_22
v1 = T_IsBoundedJoinSemilattice_116 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_126 (T_IsBoundedJoinSemilattice_116 -> T_IsBoundedJoinSemilattice_116
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_116
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsJoinSemilattice_22 -> T_IsPartialOrder_174
d_isPartialOrder_30 (T_IsJoinSemilattice_22 -> T_IsJoinSemilattice_22
forall a b. a -> b
coe T_IsJoinSemilattice_22
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'_116
            ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_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) ->
  AgdaAny ->
  T_IsBoundedJoinSemilattice_116 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_158 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedJoinSemilattice_116
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_158 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7
                                    T_IsBoundedJoinSemilattice_116
v8
  = T_IsBoundedJoinSemilattice_116
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_158 T_IsBoundedJoinSemilattice_116
v8
du_'8764''45'resp'737''45''8776'_158 ::
  T_IsBoundedJoinSemilattice_116 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_158 :: T_IsBoundedJoinSemilattice_116
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_158 T_IsBoundedJoinSemilattice_116
v0
  = let v1 :: T_IsJoinSemilattice_22
v1 = T_IsBoundedJoinSemilattice_116 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_126 (T_IsBoundedJoinSemilattice_116 -> T_IsBoundedJoinSemilattice_116
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_116
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsJoinSemilattice_22 -> T_IsPartialOrder_174
d_isPartialOrder_30 (T_IsJoinSemilattice_22 -> T_IsJoinSemilattice_22
forall a b. a -> b
coe T_IsJoinSemilattice_22
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'_114
            ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.≲-resp-≈
d_'8818''45'resp'45''8776'_160 ::
  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_116 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8818''45'resp'45''8776'_160 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedJoinSemilattice_116
-> T_Σ_14
d_'8818''45'resp'45''8776'_160 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedJoinSemilattice_116
v8
  = T_IsBoundedJoinSemilattice_116 -> T_Σ_14
du_'8818''45'resp'45''8776'_160 T_IsBoundedJoinSemilattice_116
v8
du_'8818''45'resp'45''8776'_160 ::
  T_IsBoundedJoinSemilattice_116 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8818''45'resp'45''8776'_160 :: T_IsBoundedJoinSemilattice_116 -> T_Σ_14
du_'8818''45'resp'45''8776'_160 T_IsBoundedJoinSemilattice_116
v0
  = let v1 :: T_IsJoinSemilattice_22
v1 = T_IsBoundedJoinSemilattice_116 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_126 (T_IsBoundedJoinSemilattice_116 -> T_IsBoundedJoinSemilattice_116
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_116
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsJoinSemilattice_22 -> T_IsPartialOrder_174
d_isPartialOrder_30 (T_IsJoinSemilattice_22 -> T_IsJoinSemilattice_22
forall a b. a -> b
coe T_IsJoinSemilattice_22
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_'8818''45'resp'45''8776'_112
            ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.≲-respʳ-≈
d_'8818''45'resp'691''45''8776'_162 ::
  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_116 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'691''45''8776'_162 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedJoinSemilattice_116
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'691''45''8776'_162 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7
                                    T_IsBoundedJoinSemilattice_116
v8
  = T_IsBoundedJoinSemilattice_116
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_162 T_IsBoundedJoinSemilattice_116
v8
du_'8818''45'resp'691''45''8776'_162 ::
  T_IsBoundedJoinSemilattice_116 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_162 :: T_IsBoundedJoinSemilattice_116
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_162 T_IsBoundedJoinSemilattice_116
v0
  = let v1 :: T_IsJoinSemilattice_22
v1 = T_IsBoundedJoinSemilattice_116 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_126 (T_IsBoundedJoinSemilattice_116 -> T_IsBoundedJoinSemilattice_116
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_116
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsJoinSemilattice_22 -> T_IsPartialOrder_174
d_isPartialOrder_30 (T_IsJoinSemilattice_22 -> T_IsJoinSemilattice_22
forall a b. a -> b
coe T_IsJoinSemilattice_22
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_'8818''45'resp'691''45''8776'_106
            ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.≲-respˡ-≈
d_'8818''45'resp'737''45''8776'_164 ::
  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_116 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'737''45''8776'_164 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedJoinSemilattice_116
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'737''45''8776'_164 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7
                                    T_IsBoundedJoinSemilattice_116
v8
  = T_IsBoundedJoinSemilattice_116
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_164 T_IsBoundedJoinSemilattice_116
v8
du_'8818''45'resp'737''45''8776'_164 ::
  T_IsBoundedJoinSemilattice_116 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_164 :: T_IsBoundedJoinSemilattice_116
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_164 T_IsBoundedJoinSemilattice_116
v0
  = let v1 :: T_IsJoinSemilattice_22
v1 = T_IsBoundedJoinSemilattice_116 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_126 (T_IsBoundedJoinSemilattice_116 -> T_IsBoundedJoinSemilattice_116
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_116
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsJoinSemilattice_22 -> T_IsPartialOrder_174
d_isPartialOrder_30 (T_IsJoinSemilattice_22 -> T_IsJoinSemilattice_22
forall a b. a -> b
coe T_IsJoinSemilattice_22
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_'8818''45'resp'737''45''8776'_100
            ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.Eq.isPartialEquivalence
d_isPartialEquivalence_168 ::
  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_116 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_168 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedJoinSemilattice_116
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_168 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedJoinSemilattice_116
v8
  = T_IsBoundedJoinSemilattice_116 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_168 T_IsBoundedJoinSemilattice_116
v8
du_isPartialEquivalence_168 ::
  T_IsBoundedJoinSemilattice_116 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_168 :: T_IsBoundedJoinSemilattice_116 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_168 T_IsBoundedJoinSemilattice_116
v0
  = let v1 :: T_IsJoinSemilattice_22
v1 = T_IsBoundedJoinSemilattice_116 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_126 (T_IsBoundedJoinSemilattice_116 -> T_IsBoundedJoinSemilattice_116
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_116
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsJoinSemilattice_22 -> T_IsPartialOrder_174
d_isPartialOrder_30 (T_IsJoinSemilattice_22 -> T_IsJoinSemilattice_22
forall a b. a -> b
coe T_IsJoinSemilattice_22
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreorder_70
v3
                = T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                    (T_IsPartialOrder_174 -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsPartialOrder_174
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.Structures.IsBoundedJoinSemilattice._.Eq.refl
d_refl_170 :: T_IsBoundedJoinSemilattice_116 -> AgdaAny -> AgdaAny
d_refl_170 :: T_IsBoundedJoinSemilattice_116 -> AgdaAny -> AgdaAny
d_refl_170 T_IsBoundedJoinSemilattice_116
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsJoinSemilattice_22 -> T_IsPartialOrder_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> T_IsPartialOrder_174
d_isPartialOrder_30 ((T_IsBoundedJoinSemilattice_116 -> T_IsJoinSemilattice_22)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_116 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_126 (T_IsBoundedJoinSemilattice_116 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_116
v0)))))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.Eq.reflexive
d_reflexive_172 ::
  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_116 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_172 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedJoinSemilattice_116
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_172 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedJoinSemilattice_116
v8
  = T_IsBoundedJoinSemilattice_116
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_172 T_IsBoundedJoinSemilattice_116
v8
du_reflexive_172 ::
  T_IsBoundedJoinSemilattice_116 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_172 :: T_IsBoundedJoinSemilattice_116
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_172 T_IsBoundedJoinSemilattice_116
v0
  = let v1 :: T_IsJoinSemilattice_22
v1 = T_IsBoundedJoinSemilattice_116 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_126 (T_IsBoundedJoinSemilattice_116 -> T_IsBoundedJoinSemilattice_116
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_116
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsJoinSemilattice_22 -> T_IsPartialOrder_174
d_isPartialOrder_30 (T_IsJoinSemilattice_22 -> T_IsJoinSemilattice_22
forall a b. a -> b
coe T_IsJoinSemilattice_22
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreorder_70
v3
                = T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                    (T_IsPartialOrder_174 -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsPartialOrder_174
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.Structures.IsBoundedJoinSemilattice._.Eq.sym
d_sym_174 ::
  T_IsBoundedJoinSemilattice_116 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_174 :: T_IsBoundedJoinSemilattice_116
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_174 T_IsBoundedJoinSemilattice_116
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsJoinSemilattice_22 -> T_IsPartialOrder_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> T_IsPartialOrder_174
d_isPartialOrder_30 ((T_IsBoundedJoinSemilattice_116 -> T_IsJoinSemilattice_22)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_116 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_126 (T_IsBoundedJoinSemilattice_116 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_116
v0)))))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.Eq.trans
d_trans_176 ::
  T_IsBoundedJoinSemilattice_116 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_176 :: T_IsBoundedJoinSemilattice_116
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_176 T_IsBoundedJoinSemilattice_116
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsJoinSemilattice_22 -> T_IsPartialOrder_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> T_IsPartialOrder_174
d_isPartialOrder_30 ((T_IsBoundedJoinSemilattice_116 -> T_IsJoinSemilattice_22)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_116 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_126 (T_IsBoundedJoinSemilattice_116 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_116
v0)))))
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice
d_IsMeetSemilattice_180 :: p -> p -> p -> p -> p -> p -> p -> ()
d_IsMeetSemilattice_180 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsMeetSemilattice_180
  = C_IsMeetSemilattice'46'constructor_7577 MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_174
                                            (AgdaAny ->
                                             AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14)
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice.isPartialOrder
d_isPartialOrder_188 ::
  T_IsMeetSemilattice_180 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_174
d_isPartialOrder_188 :: T_IsMeetSemilattice_180 -> T_IsPartialOrder_174
d_isPartialOrder_188 T_IsMeetSemilattice_180
v0
  = case T_IsMeetSemilattice_180 -> T_IsMeetSemilattice_180
forall a b. a -> b
coe T_IsMeetSemilattice_180
v0 of
      C_IsMeetSemilattice'46'constructor_7577 T_IsPartialOrder_174
v1 AgdaAny -> AgdaAny -> T_Σ_14
v2 -> T_IsPartialOrder_174 -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsPartialOrder_174
v1
      T_IsMeetSemilattice_180
_ -> T_IsPartialOrder_174
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice.infimum
d_infimum_190 ::
  T_IsMeetSemilattice_180 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_infimum_190 :: T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_190 T_IsMeetSemilattice_180
v0
  = case T_IsMeetSemilattice_180 -> T_IsMeetSemilattice_180
forall a b. a -> b
coe T_IsMeetSemilattice_180
v0 of
      C_IsMeetSemilattice'46'constructor_7577 T_IsPartialOrder_174
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_180
_ -> AgdaAny -> AgdaAny -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice.x∧y≤x
d_x'8743'y'8804'x_196 ::
  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_180 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'x_196 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMeetSemilattice_180
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'x_196 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsMeetSemilattice_180
v7 AgdaAny
v8 AgdaAny
v9
  = T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_196 T_IsMeetSemilattice_180
v7 AgdaAny
v8 AgdaAny
v9
du_x'8743'y'8804'x_196 ::
  T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_196 :: T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_196 T_IsMeetSemilattice_180
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_180 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_190 T_IsMeetSemilattice_180
v0 AgdaAny
v1 AgdaAny
v2)
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice.x∧y≤y
d_x'8743'y'8804'y_208 ::
  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_180 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'y_208 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMeetSemilattice_180
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'y_208 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsMeetSemilattice_180
v7 AgdaAny
v8 AgdaAny
v9
  = T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_208 T_IsMeetSemilattice_180
v7 AgdaAny
v8 AgdaAny
v9
du_x'8743'y'8804'y_208 ::
  T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_208 :: T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_208 T_IsMeetSemilattice_180
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_180 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_190 T_IsMeetSemilattice_180
v0 AgdaAny
v1 AgdaAny
v2))
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice.∧-greatest
d_'8743''45'greatest_222 ::
  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_180 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'greatest_222 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMeetSemilattice_180
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'greatest_222 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsMeetSemilattice_180
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
  = T_IsMeetSemilattice_180
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_222 T_IsMeetSemilattice_180
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
du_'8743''45'greatest_222 ::
  T_IsMeetSemilattice_180 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_222 :: T_IsMeetSemilattice_180
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_222 T_IsMeetSemilattice_180
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_180 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_190 T_IsMeetSemilattice_180
v0 AgdaAny
v2 AgdaAny
v3))
      AgdaAny
v1
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice._.antisym
d_antisym_234 ::
  T_IsMeetSemilattice_180 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_234 :: T_IsMeetSemilattice_180
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_234 T_IsMeetSemilattice_180
v0
  = (T_IsPartialOrder_174
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_174
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_184
      ((T_IsMeetSemilattice_180 -> T_IsPartialOrder_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_180 -> T_IsPartialOrder_174
d_isPartialOrder_188 (T_IsMeetSemilattice_180 -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_180
v0))
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice._.isEquivalence
d_isEquivalence_236 ::
  T_IsMeetSemilattice_180 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_236 :: T_IsMeetSemilattice_180 -> T_IsEquivalence_26
d_isEquivalence_236 T_IsMeetSemilattice_180
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsMeetSemilattice_180 -> T_IsPartialOrder_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_180 -> T_IsPartialOrder_174
d_isPartialOrder_188 (T_IsMeetSemilattice_180 -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_180
v0)))
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice._.isPreorder
d_isPreorder_238 ::
  T_IsMeetSemilattice_180 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_238 :: T_IsMeetSemilattice_180 -> T_IsPreorder_70
d_isPreorder_238 T_IsMeetSemilattice_180
v0
  = (T_IsPartialOrder_174 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
      ((T_IsMeetSemilattice_180 -> T_IsPartialOrder_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_180 -> T_IsPartialOrder_174
d_isPartialOrder_188 (T_IsMeetSemilattice_180 -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_180
v0))
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice._.refl
d_refl_240 ::
  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_180 -> AgdaAny -> AgdaAny
d_refl_240 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMeetSemilattice_180
-> AgdaAny
-> AgdaAny
d_refl_240 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsMeetSemilattice_180
v7 = T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny
du_refl_240 T_IsMeetSemilattice_180
v7
du_refl_240 :: T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny
du_refl_240 :: T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny
du_refl_240 T_IsMeetSemilattice_180
v0
  = let v1 :: T_IsPartialOrder_174
v1 = T_IsMeetSemilattice_180 -> T_IsPartialOrder_174
d_isPartialOrder_188 (T_IsMeetSemilattice_180 -> T_IsMeetSemilattice_180
forall a b. a -> b
coe T_IsMeetSemilattice_180
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182 (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v1)))
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice._.reflexive
d_reflexive_242 ::
  T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_242 :: T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_242 T_IsMeetSemilattice_180
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsMeetSemilattice_180 -> T_IsPartialOrder_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_180 -> T_IsPartialOrder_174
d_isPartialOrder_188 (T_IsMeetSemilattice_180 -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_180
v0)))
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice._.trans
d_trans_244 ::
  T_IsMeetSemilattice_180 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_244 :: T_IsMeetSemilattice_180
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_244 T_IsMeetSemilattice_180
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsMeetSemilattice_180 -> T_IsPartialOrder_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_180 -> T_IsPartialOrder_174
d_isPartialOrder_188 (T_IsMeetSemilattice_180 -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_180
v0)))
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice._.∼-resp-≈
d_'8764''45'resp'45''8776'_246 ::
  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_180 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_246 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMeetSemilattice_180
-> T_Σ_14
d_'8764''45'resp'45''8776'_246 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsMeetSemilattice_180
v7
  = T_IsMeetSemilattice_180 -> T_Σ_14
du_'8764''45'resp'45''8776'_246 T_IsMeetSemilattice_180
v7
du_'8764''45'resp'45''8776'_246 ::
  T_IsMeetSemilattice_180 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_246 :: T_IsMeetSemilattice_180 -> T_Σ_14
du_'8764''45'resp'45''8776'_246 T_IsMeetSemilattice_180
v0
  = let v1 :: T_IsPartialOrder_174
v1 = T_IsMeetSemilattice_180 -> T_IsPartialOrder_174
d_isPartialOrder_188 (T_IsMeetSemilattice_180 -> T_IsMeetSemilattice_180
forall a b. a -> b
coe T_IsMeetSemilattice_180
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'_118
         ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182 (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v1)))
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_248 ::
  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_180 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_248 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMeetSemilattice_180
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_248 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsMeetSemilattice_180
v7
  = T_IsMeetSemilattice_180
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_248 T_IsMeetSemilattice_180
v7
du_'8764''45'resp'691''45''8776'_248 ::
  T_IsMeetSemilattice_180 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_248 :: T_IsMeetSemilattice_180
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_248 T_IsMeetSemilattice_180
v0
  = let v1 :: T_IsPartialOrder_174
v1 = T_IsMeetSemilattice_180 -> T_IsPartialOrder_174
d_isPartialOrder_188 (T_IsMeetSemilattice_180 -> T_IsMeetSemilattice_180
forall a b. a -> b
coe T_IsMeetSemilattice_180
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'_116
         ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182 (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v1)))
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_250 ::
  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_180 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_250 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMeetSemilattice_180
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_250 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsMeetSemilattice_180
v7
  = T_IsMeetSemilattice_180
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_250 T_IsMeetSemilattice_180
v7
du_'8764''45'resp'737''45''8776'_250 ::
  T_IsMeetSemilattice_180 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_250 :: T_IsMeetSemilattice_180
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_250 T_IsMeetSemilattice_180
v0
  = let v1 :: T_IsPartialOrder_174
v1 = T_IsMeetSemilattice_180 -> T_IsPartialOrder_174
d_isPartialOrder_188 (T_IsMeetSemilattice_180 -> T_IsMeetSemilattice_180
forall a b. a -> b
coe T_IsMeetSemilattice_180
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'_114
         ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182 (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v1)))
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice._.≲-resp-≈
d_'8818''45'resp'45''8776'_252 ::
  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_180 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8818''45'resp'45''8776'_252 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMeetSemilattice_180
-> T_Σ_14
d_'8818''45'resp'45''8776'_252 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsMeetSemilattice_180
v7
  = T_IsMeetSemilattice_180 -> T_Σ_14
du_'8818''45'resp'45''8776'_252 T_IsMeetSemilattice_180
v7
du_'8818''45'resp'45''8776'_252 ::
  T_IsMeetSemilattice_180 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8818''45'resp'45''8776'_252 :: T_IsMeetSemilattice_180 -> T_Σ_14
du_'8818''45'resp'45''8776'_252 T_IsMeetSemilattice_180
v0
  = let v1 :: T_IsPartialOrder_174
v1 = T_IsMeetSemilattice_180 -> T_IsPartialOrder_174
d_isPartialOrder_188 (T_IsMeetSemilattice_180 -> T_IsMeetSemilattice_180
forall a b. a -> b
coe T_IsMeetSemilattice_180
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_'8818''45'resp'45''8776'_112
         ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182 (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v1)))
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice._.≲-respʳ-≈
d_'8818''45'resp'691''45''8776'_254 ::
  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_180 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'691''45''8776'_254 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMeetSemilattice_180
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'691''45''8776'_254 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsMeetSemilattice_180
v7
  = T_IsMeetSemilattice_180
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_254 T_IsMeetSemilattice_180
v7
du_'8818''45'resp'691''45''8776'_254 ::
  T_IsMeetSemilattice_180 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_254 :: T_IsMeetSemilattice_180
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_254 T_IsMeetSemilattice_180
v0
  = let v1 :: T_IsPartialOrder_174
v1 = T_IsMeetSemilattice_180 -> T_IsPartialOrder_174
d_isPartialOrder_188 (T_IsMeetSemilattice_180 -> T_IsMeetSemilattice_180
forall a b. a -> b
coe T_IsMeetSemilattice_180
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_'8818''45'resp'691''45''8776'_106
         ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182 (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v1)))
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice._.≲-respˡ-≈
d_'8818''45'resp'737''45''8776'_256 ::
  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_180 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'737''45''8776'_256 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMeetSemilattice_180
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'737''45''8776'_256 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsMeetSemilattice_180
v7
  = T_IsMeetSemilattice_180
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_256 T_IsMeetSemilattice_180
v7
du_'8818''45'resp'737''45''8776'_256 ::
  T_IsMeetSemilattice_180 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_256 :: T_IsMeetSemilattice_180
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_256 T_IsMeetSemilattice_180
v0
  = let v1 :: T_IsPartialOrder_174
v1 = T_IsMeetSemilattice_180 -> T_IsPartialOrder_174
d_isPartialOrder_188 (T_IsMeetSemilattice_180 -> T_IsMeetSemilattice_180
forall a b. a -> b
coe T_IsMeetSemilattice_180
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_'8818''45'resp'737''45''8776'_100
         ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182 (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v1)))
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice._.Eq.isPartialEquivalence
d_isPartialEquivalence_260 ::
  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_180 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_260 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMeetSemilattice_180
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_260 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsMeetSemilattice_180
v7
  = T_IsMeetSemilattice_180 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_260 T_IsMeetSemilattice_180
v7
du_isPartialEquivalence_260 ::
  T_IsMeetSemilattice_180 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_260 :: T_IsMeetSemilattice_180 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_260 T_IsMeetSemilattice_180
v0
  = let v1 :: T_IsPartialOrder_174
v1 = T_IsMeetSemilattice_180 -> T_IsPartialOrder_174
d_isPartialOrder_188 (T_IsMeetSemilattice_180 -> T_IsMeetSemilattice_180
forall a b. a -> b
coe T_IsMeetSemilattice_180
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPreorder_70
v2
             = T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                 (T_IsPartialOrder_174 -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsPartialOrder_174
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.Structures.IsMeetSemilattice._.Eq.refl
d_refl_262 :: T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny
d_refl_262 :: T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny
d_refl_262 T_IsMeetSemilattice_180
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsMeetSemilattice_180 -> T_IsPartialOrder_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_180 -> T_IsPartialOrder_174
d_isPartialOrder_188 (T_IsMeetSemilattice_180 -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_180
v0))))
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice._.Eq.reflexive
d_reflexive_264 ::
  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_180 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_264 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMeetSemilattice_180
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_264 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsMeetSemilattice_180
v7
  = T_IsMeetSemilattice_180
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_264 T_IsMeetSemilattice_180
v7
du_reflexive_264 ::
  T_IsMeetSemilattice_180 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_264 :: T_IsMeetSemilattice_180
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_264 T_IsMeetSemilattice_180
v0
  = let v1 :: T_IsPartialOrder_174
v1 = T_IsMeetSemilattice_180 -> T_IsPartialOrder_174
d_isPartialOrder_188 (T_IsMeetSemilattice_180 -> T_IsMeetSemilattice_180
forall a b. a -> b
coe T_IsMeetSemilattice_180
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPreorder_70
v2
             = T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                 (T_IsPartialOrder_174 -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsPartialOrder_174
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.Structures.IsMeetSemilattice._.Eq.sym
d_sym_266 ::
  T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_266 :: T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_266 T_IsMeetSemilattice_180
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsMeetSemilattice_180 -> T_IsPartialOrder_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_180 -> T_IsPartialOrder_174
d_isPartialOrder_188 (T_IsMeetSemilattice_180 -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_180
v0))))
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice._.Eq.trans
d_trans_268 ::
  T_IsMeetSemilattice_180 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_268 :: T_IsMeetSemilattice_180
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_268 T_IsMeetSemilattice_180
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsMeetSemilattice_180 -> T_IsPartialOrder_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_180 -> T_IsPartialOrder_174
d_isPartialOrder_188 (T_IsMeetSemilattice_180 -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_180
v0))))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice
d_IsBoundedMeetSemilattice_274 :: p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsBoundedMeetSemilattice_274 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 = ()
data T_IsBoundedMeetSemilattice_274
  = C_IsBoundedMeetSemilattice'46'constructor_12265 T_IsMeetSemilattice_180
                                                    (AgdaAny -> AgdaAny)
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice.isMeetSemilattice
d_isMeetSemilattice_284 ::
  T_IsBoundedMeetSemilattice_274 -> T_IsMeetSemilattice_180
d_isMeetSemilattice_284 :: T_IsBoundedMeetSemilattice_274 -> T_IsMeetSemilattice_180
d_isMeetSemilattice_284 T_IsBoundedMeetSemilattice_274
v0
  = case T_IsBoundedMeetSemilattice_274 -> T_IsBoundedMeetSemilattice_274
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_274
v0 of
      C_IsBoundedMeetSemilattice'46'constructor_12265 T_IsMeetSemilattice_180
v1 AgdaAny -> AgdaAny
v2 -> T_IsMeetSemilattice_180 -> T_IsMeetSemilattice_180
forall a b. a -> b
coe T_IsMeetSemilattice_180
v1
      T_IsBoundedMeetSemilattice_274
_ -> T_IsMeetSemilattice_180
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice.maximum
d_maximum_286 ::
  T_IsBoundedMeetSemilattice_274 -> AgdaAny -> AgdaAny
d_maximum_286 :: T_IsBoundedMeetSemilattice_274 -> AgdaAny -> AgdaAny
d_maximum_286 T_IsBoundedMeetSemilattice_274
v0
  = case T_IsBoundedMeetSemilattice_274 -> T_IsBoundedMeetSemilattice_274
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_274
v0 of
      C_IsBoundedMeetSemilattice'46'constructor_12265 T_IsMeetSemilattice_180
v1 AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_IsBoundedMeetSemilattice_274
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.antisym
d_antisym_290 ::
  T_IsBoundedMeetSemilattice_274 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_290 :: T_IsBoundedMeetSemilattice_274
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_290 T_IsBoundedMeetSemilattice_274
v0
  = (T_IsPartialOrder_174
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_174
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_184
      ((T_IsMeetSemilattice_180 -> T_IsPartialOrder_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_180 -> T_IsPartialOrder_174
d_isPartialOrder_188 ((T_IsBoundedMeetSemilattice_274 -> T_IsMeetSemilattice_180)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_274 -> T_IsMeetSemilattice_180
d_isMeetSemilattice_284 (T_IsBoundedMeetSemilattice_274 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_274
v0)))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.infimum
d_infimum_292 ::
  T_IsBoundedMeetSemilattice_274 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_infimum_292 :: T_IsBoundedMeetSemilattice_274 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_292 T_IsBoundedMeetSemilattice_274
v0
  = (T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_190 ((T_IsBoundedMeetSemilattice_274 -> T_IsMeetSemilattice_180)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_274 -> T_IsMeetSemilattice_180
d_isMeetSemilattice_284 (T_IsBoundedMeetSemilattice_274 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_274
v0))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.isEquivalence
d_isEquivalence_294 ::
  T_IsBoundedMeetSemilattice_274 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_294 :: T_IsBoundedMeetSemilattice_274 -> T_IsEquivalence_26
d_isEquivalence_294 T_IsBoundedMeetSemilattice_274
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsMeetSemilattice_180 -> T_IsPartialOrder_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_180 -> T_IsPartialOrder_174
d_isPartialOrder_188 ((T_IsBoundedMeetSemilattice_274 -> T_IsMeetSemilattice_180)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_274 -> T_IsMeetSemilattice_180
d_isMeetSemilattice_284 (T_IsBoundedMeetSemilattice_274 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_274
v0))))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.isPartialOrder
d_isPartialOrder_296 ::
  T_IsBoundedMeetSemilattice_274 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_174
d_isPartialOrder_296 :: T_IsBoundedMeetSemilattice_274 -> T_IsPartialOrder_174
d_isPartialOrder_296 T_IsBoundedMeetSemilattice_274
v0
  = (T_IsMeetSemilattice_180 -> T_IsPartialOrder_174)
-> AgdaAny -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsMeetSemilattice_180 -> T_IsPartialOrder_174
d_isPartialOrder_188 ((T_IsBoundedMeetSemilattice_274 -> T_IsMeetSemilattice_180)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_274 -> T_IsMeetSemilattice_180
d_isMeetSemilattice_284 (T_IsBoundedMeetSemilattice_274 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_274
v0))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.isPreorder
d_isPreorder_298 ::
  T_IsBoundedMeetSemilattice_274 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_298 :: T_IsBoundedMeetSemilattice_274 -> T_IsPreorder_70
d_isPreorder_298 T_IsBoundedMeetSemilattice_274
v0
  = (T_IsPartialOrder_174 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
      ((T_IsMeetSemilattice_180 -> T_IsPartialOrder_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_180 -> T_IsPartialOrder_174
d_isPartialOrder_188 ((T_IsBoundedMeetSemilattice_274 -> T_IsMeetSemilattice_180)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_274 -> T_IsMeetSemilattice_180
d_isMeetSemilattice_284 (T_IsBoundedMeetSemilattice_274 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_274
v0)))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.refl
d_refl_300 ::
  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_274 -> AgdaAny -> AgdaAny
d_refl_300 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedMeetSemilattice_274
-> AgdaAny
-> AgdaAny
d_refl_300 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedMeetSemilattice_274
v8 = T_IsBoundedMeetSemilattice_274 -> AgdaAny -> AgdaAny
du_refl_300 T_IsBoundedMeetSemilattice_274
v8
du_refl_300 :: T_IsBoundedMeetSemilattice_274 -> AgdaAny -> AgdaAny
du_refl_300 :: T_IsBoundedMeetSemilattice_274 -> AgdaAny -> AgdaAny
du_refl_300 T_IsBoundedMeetSemilattice_274
v0
  = let v1 :: T_IsMeetSemilattice_180
v1 = T_IsBoundedMeetSemilattice_274 -> T_IsMeetSemilattice_180
d_isMeetSemilattice_284 (T_IsBoundedMeetSemilattice_274 -> T_IsBoundedMeetSemilattice_274
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_274
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsMeetSemilattice_180 -> T_IsPartialOrder_174
d_isPartialOrder_188 (T_IsMeetSemilattice_180 -> T_IsMeetSemilattice_180
forall a b. a -> b
coe T_IsMeetSemilattice_180
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.reflexive
d_reflexive_302 ::
  T_IsBoundedMeetSemilattice_274 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_302 :: T_IsBoundedMeetSemilattice_274
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_302 T_IsBoundedMeetSemilattice_274
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsMeetSemilattice_180 -> T_IsPartialOrder_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_180 -> T_IsPartialOrder_174
d_isPartialOrder_188 ((T_IsBoundedMeetSemilattice_274 -> T_IsMeetSemilattice_180)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_274 -> T_IsMeetSemilattice_180
d_isMeetSemilattice_284 (T_IsBoundedMeetSemilattice_274 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_274
v0))))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.trans
d_trans_304 ::
  T_IsBoundedMeetSemilattice_274 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_304 :: T_IsBoundedMeetSemilattice_274
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_304 T_IsBoundedMeetSemilattice_274
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsMeetSemilattice_180 -> T_IsPartialOrder_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_180 -> T_IsPartialOrder_174
d_isPartialOrder_188 ((T_IsBoundedMeetSemilattice_274 -> T_IsMeetSemilattice_180)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_274 -> T_IsMeetSemilattice_180
d_isMeetSemilattice_284 (T_IsBoundedMeetSemilattice_274 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_274
v0))))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.x∧y≤x
d_x'8743'y'8804'x_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_IsBoundedMeetSemilattice_274 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'x_306 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedMeetSemilattice_274
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'x_306 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedMeetSemilattice_274
v8
  = T_IsBoundedMeetSemilattice_274 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_306 T_IsBoundedMeetSemilattice_274
v8
du_x'8743'y'8804'x_306 ::
  T_IsBoundedMeetSemilattice_274 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_306 :: T_IsBoundedMeetSemilattice_274 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_306 T_IsBoundedMeetSemilattice_274
v0
  = (T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_196 ((T_IsBoundedMeetSemilattice_274 -> T_IsMeetSemilattice_180)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_274 -> T_IsMeetSemilattice_180
d_isMeetSemilattice_284 (T_IsBoundedMeetSemilattice_274 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_274
v0))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.x∧y≤y
d_x'8743'y'8804'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_IsBoundedMeetSemilattice_274 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'y_308 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedMeetSemilattice_274
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'y_308 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedMeetSemilattice_274
v8
  = T_IsBoundedMeetSemilattice_274 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_308 T_IsBoundedMeetSemilattice_274
v8
du_x'8743'y'8804'y_308 ::
  T_IsBoundedMeetSemilattice_274 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_308 :: T_IsBoundedMeetSemilattice_274 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_308 T_IsBoundedMeetSemilattice_274
v0
  = (T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_208 ((T_IsBoundedMeetSemilattice_274 -> T_IsMeetSemilattice_180)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_274 -> T_IsMeetSemilattice_180
d_isMeetSemilattice_284 (T_IsBoundedMeetSemilattice_274 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_274
v0))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.∧-greatest
d_'8743''45'greatest_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_IsBoundedMeetSemilattice_274 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'greatest_310 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedMeetSemilattice_274
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'greatest_310 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedMeetSemilattice_274
v8
  = T_IsBoundedMeetSemilattice_274
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_310 T_IsBoundedMeetSemilattice_274
v8
du_'8743''45'greatest_310 ::
  T_IsBoundedMeetSemilattice_274 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_310 :: T_IsBoundedMeetSemilattice_274
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_310 T_IsBoundedMeetSemilattice_274
v0
  = (T_IsMeetSemilattice_180
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMeetSemilattice_180
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_222 ((T_IsBoundedMeetSemilattice_274 -> T_IsMeetSemilattice_180)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_274 -> T_IsMeetSemilattice_180
d_isMeetSemilattice_284 (T_IsBoundedMeetSemilattice_274 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_274
v0))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.∼-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_IsBoundedMeetSemilattice_274 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_312 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedMeetSemilattice_274
-> T_Σ_14
d_'8764''45'resp'45''8776'_312 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedMeetSemilattice_274
v8
  = T_IsBoundedMeetSemilattice_274 -> T_Σ_14
du_'8764''45'resp'45''8776'_312 T_IsBoundedMeetSemilattice_274
v8
du_'8764''45'resp'45''8776'_312 ::
  T_IsBoundedMeetSemilattice_274 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_312 :: T_IsBoundedMeetSemilattice_274 -> T_Σ_14
du_'8764''45'resp'45''8776'_312 T_IsBoundedMeetSemilattice_274
v0
  = let v1 :: T_IsMeetSemilattice_180
v1 = T_IsBoundedMeetSemilattice_274 -> T_IsMeetSemilattice_180
d_isMeetSemilattice_284 (T_IsBoundedMeetSemilattice_274 -> T_IsBoundedMeetSemilattice_274
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_274
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsMeetSemilattice_180 -> T_IsPartialOrder_174
d_isPartialOrder_188 (T_IsMeetSemilattice_180 -> T_IsMeetSemilattice_180
forall a b. a -> b
coe T_IsMeetSemilattice_180
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'_118
            ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.∼-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_IsBoundedMeetSemilattice_274 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_314 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedMeetSemilattice_274
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_314 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7
                                    T_IsBoundedMeetSemilattice_274
v8
  = T_IsBoundedMeetSemilattice_274
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_314 T_IsBoundedMeetSemilattice_274
v8
du_'8764''45'resp'691''45''8776'_314 ::
  T_IsBoundedMeetSemilattice_274 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_314 :: T_IsBoundedMeetSemilattice_274
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_314 T_IsBoundedMeetSemilattice_274
v0
  = let v1 :: T_IsMeetSemilattice_180
v1 = T_IsBoundedMeetSemilattice_274 -> T_IsMeetSemilattice_180
d_isMeetSemilattice_284 (T_IsBoundedMeetSemilattice_274 -> T_IsBoundedMeetSemilattice_274
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_274
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsMeetSemilattice_180 -> T_IsPartialOrder_174
d_isPartialOrder_188 (T_IsMeetSemilattice_180 -> T_IsMeetSemilattice_180
forall a b. a -> b
coe T_IsMeetSemilattice_180
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'_116
            ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.∼-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_IsBoundedMeetSemilattice_274 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_316 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedMeetSemilattice_274
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_316 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7
                                    T_IsBoundedMeetSemilattice_274
v8
  = T_IsBoundedMeetSemilattice_274
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_316 T_IsBoundedMeetSemilattice_274
v8
du_'8764''45'resp'737''45''8776'_316 ::
  T_IsBoundedMeetSemilattice_274 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_316 :: T_IsBoundedMeetSemilattice_274
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_316 T_IsBoundedMeetSemilattice_274
v0
  = let v1 :: T_IsMeetSemilattice_180
v1 = T_IsBoundedMeetSemilattice_274 -> T_IsMeetSemilattice_180
d_isMeetSemilattice_284 (T_IsBoundedMeetSemilattice_274 -> T_IsBoundedMeetSemilattice_274
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_274
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsMeetSemilattice_180 -> T_IsPartialOrder_174
d_isPartialOrder_188 (T_IsMeetSemilattice_180 -> T_IsMeetSemilattice_180
forall a b. a -> b
coe T_IsMeetSemilattice_180
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'_114
            ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.≲-resp-≈
d_'8818''45'resp'45''8776'_318 ::
  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_274 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8818''45'resp'45''8776'_318 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedMeetSemilattice_274
-> T_Σ_14
d_'8818''45'resp'45''8776'_318 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedMeetSemilattice_274
v8
  = T_IsBoundedMeetSemilattice_274 -> T_Σ_14
du_'8818''45'resp'45''8776'_318 T_IsBoundedMeetSemilattice_274
v8
du_'8818''45'resp'45''8776'_318 ::
  T_IsBoundedMeetSemilattice_274 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8818''45'resp'45''8776'_318 :: T_IsBoundedMeetSemilattice_274 -> T_Σ_14
du_'8818''45'resp'45''8776'_318 T_IsBoundedMeetSemilattice_274
v0
  = let v1 :: T_IsMeetSemilattice_180
v1 = T_IsBoundedMeetSemilattice_274 -> T_IsMeetSemilattice_180
d_isMeetSemilattice_284 (T_IsBoundedMeetSemilattice_274 -> T_IsBoundedMeetSemilattice_274
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_274
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsMeetSemilattice_180 -> T_IsPartialOrder_174
d_isPartialOrder_188 (T_IsMeetSemilattice_180 -> T_IsMeetSemilattice_180
forall a b. a -> b
coe T_IsMeetSemilattice_180
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_'8818''45'resp'45''8776'_112
            ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.≲-respʳ-≈
d_'8818''45'resp'691''45''8776'_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_IsBoundedMeetSemilattice_274 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'691''45''8776'_320 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedMeetSemilattice_274
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'691''45''8776'_320 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7
                                    T_IsBoundedMeetSemilattice_274
v8
  = T_IsBoundedMeetSemilattice_274
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_320 T_IsBoundedMeetSemilattice_274
v8
du_'8818''45'resp'691''45''8776'_320 ::
  T_IsBoundedMeetSemilattice_274 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_320 :: T_IsBoundedMeetSemilattice_274
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_320 T_IsBoundedMeetSemilattice_274
v0
  = let v1 :: T_IsMeetSemilattice_180
v1 = T_IsBoundedMeetSemilattice_274 -> T_IsMeetSemilattice_180
d_isMeetSemilattice_284 (T_IsBoundedMeetSemilattice_274 -> T_IsBoundedMeetSemilattice_274
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_274
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsMeetSemilattice_180 -> T_IsPartialOrder_174
d_isPartialOrder_188 (T_IsMeetSemilattice_180 -> T_IsMeetSemilattice_180
forall a b. a -> b
coe T_IsMeetSemilattice_180
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_'8818''45'resp'691''45''8776'_106
            ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.≲-respˡ-≈
d_'8818''45'resp'737''45''8776'_322 ::
  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_274 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'737''45''8776'_322 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedMeetSemilattice_274
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'737''45''8776'_322 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7
                                    T_IsBoundedMeetSemilattice_274
v8
  = T_IsBoundedMeetSemilattice_274
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_322 T_IsBoundedMeetSemilattice_274
v8
du_'8818''45'resp'737''45''8776'_322 ::
  T_IsBoundedMeetSemilattice_274 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_322 :: T_IsBoundedMeetSemilattice_274
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_322 T_IsBoundedMeetSemilattice_274
v0
  = let v1 :: T_IsMeetSemilattice_180
v1 = T_IsBoundedMeetSemilattice_274 -> T_IsMeetSemilattice_180
d_isMeetSemilattice_284 (T_IsBoundedMeetSemilattice_274 -> T_IsBoundedMeetSemilattice_274
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_274
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsMeetSemilattice_180 -> T_IsPartialOrder_174
d_isPartialOrder_188 (T_IsMeetSemilattice_180 -> T_IsMeetSemilattice_180
forall a b. a -> b
coe T_IsMeetSemilattice_180
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_'8818''45'resp'737''45''8776'_100
            ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.Eq.isPartialEquivalence
d_isPartialEquivalence_326 ::
  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_274 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_326 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedMeetSemilattice_274
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_326 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedMeetSemilattice_274
v8
  = T_IsBoundedMeetSemilattice_274 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_326 T_IsBoundedMeetSemilattice_274
v8
du_isPartialEquivalence_326 ::
  T_IsBoundedMeetSemilattice_274 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_326 :: T_IsBoundedMeetSemilattice_274 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_326 T_IsBoundedMeetSemilattice_274
v0
  = let v1 :: T_IsMeetSemilattice_180
v1 = T_IsBoundedMeetSemilattice_274 -> T_IsMeetSemilattice_180
d_isMeetSemilattice_284 (T_IsBoundedMeetSemilattice_274 -> T_IsBoundedMeetSemilattice_274
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_274
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsMeetSemilattice_180 -> T_IsPartialOrder_174
d_isPartialOrder_188 (T_IsMeetSemilattice_180 -> T_IsMeetSemilattice_180
forall a b. a -> b
coe T_IsMeetSemilattice_180
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreorder_70
v3
                = T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                    (T_IsPartialOrder_174 -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsPartialOrder_174
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.Structures.IsBoundedMeetSemilattice._.Eq.refl
d_refl_328 :: T_IsBoundedMeetSemilattice_274 -> AgdaAny -> AgdaAny
d_refl_328 :: T_IsBoundedMeetSemilattice_274 -> AgdaAny -> AgdaAny
d_refl_328 T_IsBoundedMeetSemilattice_274
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsMeetSemilattice_180 -> T_IsPartialOrder_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_180 -> T_IsPartialOrder_174
d_isPartialOrder_188 ((T_IsBoundedMeetSemilattice_274 -> T_IsMeetSemilattice_180)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_274 -> T_IsMeetSemilattice_180
d_isMeetSemilattice_284 (T_IsBoundedMeetSemilattice_274 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_274
v0)))))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.Eq.reflexive
d_reflexive_330 ::
  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_274 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_330 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedMeetSemilattice_274
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_330 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedMeetSemilattice_274
v8
  = T_IsBoundedMeetSemilattice_274
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_330 T_IsBoundedMeetSemilattice_274
v8
du_reflexive_330 ::
  T_IsBoundedMeetSemilattice_274 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_330 :: T_IsBoundedMeetSemilattice_274
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_330 T_IsBoundedMeetSemilattice_274
v0
  = let v1 :: T_IsMeetSemilattice_180
v1 = T_IsBoundedMeetSemilattice_274 -> T_IsMeetSemilattice_180
d_isMeetSemilattice_284 (T_IsBoundedMeetSemilattice_274 -> T_IsBoundedMeetSemilattice_274
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_274
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsMeetSemilattice_180 -> T_IsPartialOrder_174
d_isPartialOrder_188 (T_IsMeetSemilattice_180 -> T_IsMeetSemilattice_180
forall a b. a -> b
coe T_IsMeetSemilattice_180
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreorder_70
v3
                = T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                    (T_IsPartialOrder_174 -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsPartialOrder_174
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.Structures.IsBoundedMeetSemilattice._.Eq.sym
d_sym_332 ::
  T_IsBoundedMeetSemilattice_274 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_332 :: T_IsBoundedMeetSemilattice_274
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_332 T_IsBoundedMeetSemilattice_274
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsMeetSemilattice_180 -> T_IsPartialOrder_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_180 -> T_IsPartialOrder_174
d_isPartialOrder_188 ((T_IsBoundedMeetSemilattice_274 -> T_IsMeetSemilattice_180)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_274 -> T_IsMeetSemilattice_180
d_isMeetSemilattice_284 (T_IsBoundedMeetSemilattice_274 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_274
v0)))))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.Eq.trans
d_trans_334 ::
  T_IsBoundedMeetSemilattice_274 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_334 :: T_IsBoundedMeetSemilattice_274
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_334 T_IsBoundedMeetSemilattice_274
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsMeetSemilattice_180 -> T_IsPartialOrder_174)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_180 -> T_IsPartialOrder_174
d_isPartialOrder_188 ((T_IsBoundedMeetSemilattice_274 -> T_IsMeetSemilattice_180)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_274 -> T_IsMeetSemilattice_180
d_isMeetSemilattice_284 (T_IsBoundedMeetSemilattice_274 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_274
v0)))))
-- Relation.Binary.Lattice.Structures.IsLattice
d_IsLattice_340 :: p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsLattice_340 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 = ()
data T_IsLattice_340
  = C_IsLattice'46'constructor_14941 MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_174
                                     (AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14)
                                     (AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14)
-- Relation.Binary.Lattice.Structures.IsLattice.isPartialOrder
d_isPartialOrder_352 ::
  T_IsLattice_340 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_174
d_isPartialOrder_352 :: T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 T_IsLattice_340
v0
  = case T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
v0 of
      C_IsLattice'46'constructor_14941 T_IsPartialOrder_174
v1 AgdaAny -> AgdaAny -> T_Σ_14
v2 AgdaAny -> AgdaAny -> T_Σ_14
v3 -> T_IsPartialOrder_174 -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsPartialOrder_174
v1
      T_IsLattice_340
_ -> T_IsPartialOrder_174
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.Structures.IsLattice.supremum
d_supremum_354 ::
  T_IsLattice_340 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_supremum_354 :: T_IsLattice_340 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_354 T_IsLattice_340
v0
  = case T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
v0 of
      C_IsLattice'46'constructor_14941 T_IsPartialOrder_174
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_340
_ -> AgdaAny -> AgdaAny -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.Structures.IsLattice.infimum
d_infimum_356 ::
  T_IsLattice_340 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_infimum_356 :: T_IsLattice_340 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_356 T_IsLattice_340
v0
  = case T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
v0 of
      C_IsLattice'46'constructor_14941 T_IsPartialOrder_174
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_340
_ -> AgdaAny -> AgdaAny -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.Structures.IsLattice.isJoinSemilattice
d_isJoinSemilattice_358 ::
  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_340 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_358 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_340
-> T_IsJoinSemilattice_22
d_isJoinSemilattice_358 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsLattice_340
v8
  = T_IsLattice_340 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_358 T_IsLattice_340
v8
du_isJoinSemilattice_358 ::
  T_IsLattice_340 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_358 :: T_IsLattice_340 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_358 T_IsLattice_340
v0
  = (T_IsPartialOrder_174
 -> (AgdaAny -> AgdaAny -> T_Σ_14) -> T_IsJoinSemilattice_22)
-> AgdaAny -> AgdaAny -> T_IsJoinSemilattice_22
forall a b. a -> b
coe
      T_IsPartialOrder_174
-> (AgdaAny -> AgdaAny -> T_Σ_14) -> T_IsJoinSemilattice_22
C_IsJoinSemilattice'46'constructor_527
      ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v0)) ((T_IsLattice_340 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_354 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v0))
-- Relation.Binary.Lattice.Structures.IsLattice.isMeetSemilattice
d_isMeetSemilattice_360 ::
  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_340 -> T_IsMeetSemilattice_180
d_isMeetSemilattice_360 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_340
-> T_IsMeetSemilattice_180
d_isMeetSemilattice_360 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsLattice_340
v8
  = T_IsLattice_340 -> T_IsMeetSemilattice_180
du_isMeetSemilattice_360 T_IsLattice_340
v8
du_isMeetSemilattice_360 ::
  T_IsLattice_340 -> T_IsMeetSemilattice_180
du_isMeetSemilattice_360 :: T_IsLattice_340 -> T_IsMeetSemilattice_180
du_isMeetSemilattice_360 T_IsLattice_340
v0
  = (T_IsPartialOrder_174
 -> (AgdaAny -> AgdaAny -> T_Σ_14) -> T_IsMeetSemilattice_180)
-> AgdaAny -> AgdaAny -> T_IsMeetSemilattice_180
forall a b. a -> b
coe
      T_IsPartialOrder_174
-> (AgdaAny -> AgdaAny -> T_Σ_14) -> T_IsMeetSemilattice_180
C_IsMeetSemilattice'46'constructor_7577
      ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v0)) ((T_IsLattice_340 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_356 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v0))
-- Relation.Binary.Lattice.Structures.IsLattice._.x≤x∨y
d_x'8804'x'8744'y_364 ::
  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_340 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8804'x'8744'y_364 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_340
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8804'x'8744'y_364 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsLattice_340
v8
  = T_IsLattice_340 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_364 T_IsLattice_340
v8
du_x'8804'x'8744'y_364 ::
  T_IsLattice_340 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_364 :: T_IsLattice_340 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_364 T_IsLattice_340
v0
  = (T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_38 ((T_IsLattice_340 -> T_IsJoinSemilattice_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_358 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v0))
-- Relation.Binary.Lattice.Structures.IsLattice._.y≤x∨y
d_y'8804'x'8744'y_366 ::
  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_340 -> AgdaAny -> AgdaAny -> AgdaAny
d_y'8804'x'8744'y_366 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_340
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_y'8804'x'8744'y_366 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsLattice_340
v8
  = T_IsLattice_340 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_366 T_IsLattice_340
v8
du_y'8804'x'8744'y_366 ::
  T_IsLattice_340 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_366 :: T_IsLattice_340 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_366 T_IsLattice_340
v0
  = (T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_50 ((T_IsLattice_340 -> T_IsJoinSemilattice_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_358 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v0))
-- Relation.Binary.Lattice.Structures.IsLattice._.∨-least
d_'8744''45'least_368 ::
  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_340 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'least_368 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_340
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'least_368 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsLattice_340
v8
  = T_IsLattice_340
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_368 T_IsLattice_340
v8
du_'8744''45'least_368 ::
  T_IsLattice_340 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_368 :: T_IsLattice_340
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_368 T_IsLattice_340
v0
  = (T_IsJoinSemilattice_22
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_64 ((T_IsLattice_340 -> T_IsJoinSemilattice_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_358 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v0))
-- Relation.Binary.Lattice.Structures.IsLattice._.x∧y≤x
d_x'8743'y'8804'x_372 ::
  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_340 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'x_372 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_340
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'x_372 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsLattice_340
v8
  = T_IsLattice_340 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_372 T_IsLattice_340
v8
du_x'8743'y'8804'x_372 ::
  T_IsLattice_340 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_372 :: T_IsLattice_340 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_372 T_IsLattice_340
v0
  = (T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_196 ((T_IsLattice_340 -> T_IsMeetSemilattice_180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsMeetSemilattice_180
du_isMeetSemilattice_360 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v0))
-- Relation.Binary.Lattice.Structures.IsLattice._.x∧y≤y
d_x'8743'y'8804'y_374 ::
  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_340 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'y_374 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_340
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'y_374 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsLattice_340
v8
  = T_IsLattice_340 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_374 T_IsLattice_340
v8
du_x'8743'y'8804'y_374 ::
  T_IsLattice_340 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_374 :: T_IsLattice_340 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_374 T_IsLattice_340
v0
  = (T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_208 ((T_IsLattice_340 -> T_IsMeetSemilattice_180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsMeetSemilattice_180
du_isMeetSemilattice_360 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v0))
-- Relation.Binary.Lattice.Structures.IsLattice._.∧-greatest
d_'8743''45'greatest_376 ::
  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_340 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'greatest_376 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_340
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'greatest_376 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsLattice_340
v8
  = T_IsLattice_340
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_376 T_IsLattice_340
v8
du_'8743''45'greatest_376 ::
  T_IsLattice_340 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_376 :: T_IsLattice_340
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_376 T_IsLattice_340
v0
  = (T_IsMeetSemilattice_180
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMeetSemilattice_180
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_222 ((T_IsLattice_340 -> T_IsMeetSemilattice_180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsMeetSemilattice_180
du_isMeetSemilattice_360 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v0))
-- Relation.Binary.Lattice.Structures.IsLattice._.antisym
d_antisym_380 ::
  T_IsLattice_340 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_380 :: T_IsLattice_340
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_380 T_IsLattice_340
v0
  = (T_IsPartialOrder_174
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_174
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_184
      ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v0))
-- Relation.Binary.Lattice.Structures.IsLattice._.isEquivalence
d_isEquivalence_382 ::
  T_IsLattice_340 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_382 :: T_IsLattice_340 -> T_IsEquivalence_26
d_isEquivalence_382 T_IsLattice_340
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v0)))
-- Relation.Binary.Lattice.Structures.IsLattice._.isPreorder
d_isPreorder_384 ::
  T_IsLattice_340 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_384 :: T_IsLattice_340 -> T_IsPreorder_70
d_isPreorder_384 T_IsLattice_340
v0
  = (T_IsPartialOrder_174 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
      ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v0))
-- Relation.Binary.Lattice.Structures.IsLattice._.refl
d_refl_386 ::
  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_340 -> AgdaAny -> AgdaAny
d_refl_386 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_340
-> AgdaAny
-> AgdaAny
d_refl_386 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsLattice_340
v8 = T_IsLattice_340 -> AgdaAny -> AgdaAny
du_refl_386 T_IsLattice_340
v8
du_refl_386 :: T_IsLattice_340 -> AgdaAny -> AgdaAny
du_refl_386 :: T_IsLattice_340 -> AgdaAny -> AgdaAny
du_refl_386 T_IsLattice_340
v0
  = let v1 :: T_IsPartialOrder_174
v1 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182 (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v1)))
-- Relation.Binary.Lattice.Structures.IsLattice._.reflexive
d_reflexive_388 ::
  T_IsLattice_340 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_388 :: T_IsLattice_340 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_388 T_IsLattice_340
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v0)))
-- Relation.Binary.Lattice.Structures.IsLattice._.trans
d_trans_390 ::
  T_IsLattice_340 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_390 :: T_IsLattice_340
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_390 T_IsLattice_340
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v0)))
-- Relation.Binary.Lattice.Structures.IsLattice._.∼-resp-≈
d_'8764''45'resp'45''8776'_392 ::
  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_340 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_392 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_340
-> T_Σ_14
d_'8764''45'resp'45''8776'_392 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsLattice_340
v8
  = T_IsLattice_340 -> T_Σ_14
du_'8764''45'resp'45''8776'_392 T_IsLattice_340
v8
du_'8764''45'resp'45''8776'_392 ::
  T_IsLattice_340 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_392 :: T_IsLattice_340 -> T_Σ_14
du_'8764''45'resp'45''8776'_392 T_IsLattice_340
v0
  = let v1 :: T_IsPartialOrder_174
v1 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
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'_118
         ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182 (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v1)))
-- Relation.Binary.Lattice.Structures.IsLattice._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_394 ::
  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_340 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_394 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_340
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_394 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7
                                    T_IsLattice_340
v8
  = T_IsLattice_340
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_394 T_IsLattice_340
v8
du_'8764''45'resp'691''45''8776'_394 ::
  T_IsLattice_340 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_394 :: T_IsLattice_340
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_394 T_IsLattice_340
v0
  = let v1 :: T_IsPartialOrder_174
v1 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
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'_116
         ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182 (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v1)))
-- Relation.Binary.Lattice.Structures.IsLattice._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_396 ::
  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_340 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_396 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_340
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_396 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7
                                    T_IsLattice_340
v8
  = T_IsLattice_340
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_396 T_IsLattice_340
v8
du_'8764''45'resp'737''45''8776'_396 ::
  T_IsLattice_340 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_396 :: T_IsLattice_340
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_396 T_IsLattice_340
v0
  = let v1 :: T_IsPartialOrder_174
v1 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
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'_114
         ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182 (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v1)))
-- Relation.Binary.Lattice.Structures.IsLattice._.≲-resp-≈
d_'8818''45'resp'45''8776'_398 ::
  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_340 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8818''45'resp'45''8776'_398 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_340
-> T_Σ_14
d_'8818''45'resp'45''8776'_398 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsLattice_340
v8
  = T_IsLattice_340 -> T_Σ_14
du_'8818''45'resp'45''8776'_398 T_IsLattice_340
v8
du_'8818''45'resp'45''8776'_398 ::
  T_IsLattice_340 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8818''45'resp'45''8776'_398 :: T_IsLattice_340 -> T_Σ_14
du_'8818''45'resp'45''8776'_398 T_IsLattice_340
v0
  = let v1 :: T_IsPartialOrder_174
v1 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
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_'8818''45'resp'45''8776'_112
         ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182 (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v1)))
-- Relation.Binary.Lattice.Structures.IsLattice._.≲-respʳ-≈
d_'8818''45'resp'691''45''8776'_400 ::
  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_340 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'691''45''8776'_400 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_340
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'691''45''8776'_400 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7
                                    T_IsLattice_340
v8
  = T_IsLattice_340
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_400 T_IsLattice_340
v8
du_'8818''45'resp'691''45''8776'_400 ::
  T_IsLattice_340 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_400 :: T_IsLattice_340
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_400 T_IsLattice_340
v0
  = let v1 :: T_IsPartialOrder_174
v1 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
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_'8818''45'resp'691''45''8776'_106
         ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182 (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v1)))
-- Relation.Binary.Lattice.Structures.IsLattice._.≲-respˡ-≈
d_'8818''45'resp'737''45''8776'_402 ::
  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_340 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'737''45''8776'_402 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_340
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'737''45''8776'_402 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7
                                    T_IsLattice_340
v8
  = T_IsLattice_340
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_402 T_IsLattice_340
v8
du_'8818''45'resp'737''45''8776'_402 ::
  T_IsLattice_340 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_402 :: T_IsLattice_340
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_402 T_IsLattice_340
v0
  = let v1 :: T_IsPartialOrder_174
v1 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
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_'8818''45'resp'737''45''8776'_100
         ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182 (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v1)))
-- Relation.Binary.Lattice.Structures.IsLattice._.Eq.isPartialEquivalence
d_isPartialEquivalence_406 ::
  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_340 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_406 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_340
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_406 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsLattice_340
v8
  = T_IsLattice_340 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_406 T_IsLattice_340
v8
du_isPartialEquivalence_406 ::
  T_IsLattice_340 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_406 :: T_IsLattice_340 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_406 T_IsLattice_340
v0
  = let v1 :: T_IsPartialOrder_174
v1 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPreorder_70
v2
             = T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                 (T_IsPartialOrder_174 -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsPartialOrder_174
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.Structures.IsLattice._.Eq.refl
d_refl_408 :: T_IsLattice_340 -> AgdaAny -> AgdaAny
d_refl_408 :: T_IsLattice_340 -> AgdaAny -> AgdaAny
d_refl_408 T_IsLattice_340
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v0))))
-- Relation.Binary.Lattice.Structures.IsLattice._.Eq.reflexive
d_reflexive_410 ::
  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_340 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_410 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_340
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_410 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsLattice_340
v8
  = T_IsLattice_340 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_410 T_IsLattice_340
v8
du_reflexive_410 ::
  T_IsLattice_340 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_410 :: T_IsLattice_340 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_410 T_IsLattice_340
v0
  = let v1 :: T_IsPartialOrder_174
v1 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPreorder_70
v2
             = T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                 (T_IsPartialOrder_174 -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsPartialOrder_174
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.Structures.IsLattice._.Eq.sym
d_sym_412 ::
  T_IsLattice_340 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_412 :: T_IsLattice_340 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_412 T_IsLattice_340
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v0))))
-- Relation.Binary.Lattice.Structures.IsLattice._.Eq.trans
d_trans_414 ::
  T_IsLattice_340 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_414 :: T_IsLattice_340
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_414 T_IsLattice_340
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v0))))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice
d_IsDistributiveLattice_420 :: p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsDistributiveLattice_420 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 = ()
data T_IsDistributiveLattice_420
  = C_IsDistributiveLattice'46'constructor_18193 T_IsLattice_340
                                                 (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice.isLattice
d_isLattice_430 :: T_IsDistributiveLattice_420 -> T_IsLattice_340
d_isLattice_430 :: T_IsDistributiveLattice_420 -> T_IsLattice_340
d_isLattice_430 T_IsDistributiveLattice_420
v0
  = case T_IsDistributiveLattice_420 -> T_IsDistributiveLattice_420
forall a b. a -> b
coe T_IsDistributiveLattice_420
v0 of
      C_IsDistributiveLattice'46'constructor_18193 T_IsLattice_340
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
v1
      T_IsDistributiveLattice_420
_ -> T_IsLattice_340
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice.∧-distribˡ-∨
d_'8743''45'distrib'737''45''8744'_432 ::
  T_IsDistributiveLattice_420 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'distrib'737''45''8744'_432 :: T_IsDistributiveLattice_420
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'distrib'737''45''8744'_432 T_IsDistributiveLattice_420
v0
  = case T_IsDistributiveLattice_420 -> T_IsDistributiveLattice_420
forall a b. a -> b
coe T_IsDistributiveLattice_420
v0 of
      C_IsDistributiveLattice'46'constructor_18193 T_IsLattice_340
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_420
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.antisym
d_antisym_436 ::
  T_IsDistributiveLattice_420 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_436 :: T_IsDistributiveLattice_420
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_436 T_IsDistributiveLattice_420
v0
  = (T_IsPartialOrder_174
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_174
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_184
      ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 ((T_IsDistributiveLattice_420 -> T_IsLattice_340)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_420 -> T_IsLattice_340
d_isLattice_430 (T_IsDistributiveLattice_420 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_420
v0)))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.infimum
d_infimum_438 ::
  T_IsDistributiveLattice_420 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_infimum_438 :: T_IsDistributiveLattice_420 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_438 T_IsDistributiveLattice_420
v0 = (T_IsLattice_340 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsLattice_340 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_356 ((T_IsDistributiveLattice_420 -> T_IsLattice_340)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_420 -> T_IsLattice_340
d_isLattice_430 (T_IsDistributiveLattice_420 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_420
v0))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.isEquivalence
d_isEquivalence_440 ::
  T_IsDistributiveLattice_420 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_440 :: T_IsDistributiveLattice_420 -> T_IsEquivalence_26
d_isEquivalence_440 T_IsDistributiveLattice_420
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 ((T_IsDistributiveLattice_420 -> T_IsLattice_340)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_420 -> T_IsLattice_340
d_isLattice_430 (T_IsDistributiveLattice_420 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_420
v0))))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.isJoinSemilattice
d_isJoinSemilattice_442 ::
  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_420 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_442 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_420
-> T_IsJoinSemilattice_22
d_isJoinSemilattice_442 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsDistributiveLattice_420
v8
  = T_IsDistributiveLattice_420 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_442 T_IsDistributiveLattice_420
v8
du_isJoinSemilattice_442 ::
  T_IsDistributiveLattice_420 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_442 :: T_IsDistributiveLattice_420 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_442 T_IsDistributiveLattice_420
v0
  = (T_IsLattice_340 -> T_IsJoinSemilattice_22)
-> AgdaAny -> T_IsJoinSemilattice_22
forall a b. a -> b
coe T_IsLattice_340 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_358 ((T_IsDistributiveLattice_420 -> T_IsLattice_340)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_420 -> T_IsLattice_340
d_isLattice_430 (T_IsDistributiveLattice_420 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_420
v0))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.isMeetSemilattice
d_isMeetSemilattice_444 ::
  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_420 -> T_IsMeetSemilattice_180
d_isMeetSemilattice_444 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_420
-> T_IsMeetSemilattice_180
d_isMeetSemilattice_444 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsDistributiveLattice_420
v8
  = T_IsDistributiveLattice_420 -> T_IsMeetSemilattice_180
du_isMeetSemilattice_444 T_IsDistributiveLattice_420
v8
du_isMeetSemilattice_444 ::
  T_IsDistributiveLattice_420 -> T_IsMeetSemilattice_180
du_isMeetSemilattice_444 :: T_IsDistributiveLattice_420 -> T_IsMeetSemilattice_180
du_isMeetSemilattice_444 T_IsDistributiveLattice_420
v0
  = (T_IsLattice_340 -> T_IsMeetSemilattice_180)
-> AgdaAny -> T_IsMeetSemilattice_180
forall a b. a -> b
coe T_IsLattice_340 -> T_IsMeetSemilattice_180
du_isMeetSemilattice_360 ((T_IsDistributiveLattice_420 -> T_IsLattice_340)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_420 -> T_IsLattice_340
d_isLattice_430 (T_IsDistributiveLattice_420 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_420
v0))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.isPartialOrder
d_isPartialOrder_446 ::
  T_IsDistributiveLattice_420 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_174
d_isPartialOrder_446 :: T_IsDistributiveLattice_420 -> T_IsPartialOrder_174
d_isPartialOrder_446 T_IsDistributiveLattice_420
v0
  = (T_IsLattice_340 -> T_IsPartialOrder_174)
-> AgdaAny -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 ((T_IsDistributiveLattice_420 -> T_IsLattice_340)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_420 -> T_IsLattice_340
d_isLattice_430 (T_IsDistributiveLattice_420 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_420
v0))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.isPreorder
d_isPreorder_448 ::
  T_IsDistributiveLattice_420 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_448 :: T_IsDistributiveLattice_420 -> T_IsPreorder_70
d_isPreorder_448 T_IsDistributiveLattice_420
v0
  = (T_IsPartialOrder_174 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
      ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 ((T_IsDistributiveLattice_420 -> T_IsLattice_340)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_420 -> T_IsLattice_340
d_isLattice_430 (T_IsDistributiveLattice_420 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_420
v0)))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.refl
d_refl_450 ::
  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_420 -> AgdaAny -> AgdaAny
d_refl_450 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_420
-> AgdaAny
-> AgdaAny
d_refl_450 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsDistributiveLattice_420
v8 = T_IsDistributiveLattice_420 -> AgdaAny -> AgdaAny
du_refl_450 T_IsDistributiveLattice_420
v8
du_refl_450 :: T_IsDistributiveLattice_420 -> AgdaAny -> AgdaAny
du_refl_450 :: T_IsDistributiveLattice_420 -> AgdaAny -> AgdaAny
du_refl_450 T_IsDistributiveLattice_420
v0
  = let v1 :: T_IsLattice_340
v1 = T_IsDistributiveLattice_420 -> T_IsLattice_340
d_isLattice_430 (T_IsDistributiveLattice_420 -> T_IsDistributiveLattice_420
forall a b. a -> b
coe T_IsDistributiveLattice_420
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.reflexive
d_reflexive_452 ::
  T_IsDistributiveLattice_420 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_452 :: T_IsDistributiveLattice_420
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_452 T_IsDistributiveLattice_420
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 ((T_IsDistributiveLattice_420 -> T_IsLattice_340)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_420 -> T_IsLattice_340
d_isLattice_430 (T_IsDistributiveLattice_420 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_420
v0))))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.supremum
d_supremum_454 ::
  T_IsDistributiveLattice_420 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_supremum_454 :: T_IsDistributiveLattice_420 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_454 T_IsDistributiveLattice_420
v0
  = (T_IsLattice_340 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsLattice_340 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_354 ((T_IsDistributiveLattice_420 -> T_IsLattice_340)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_420 -> T_IsLattice_340
d_isLattice_430 (T_IsDistributiveLattice_420 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_420
v0))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.trans
d_trans_456 ::
  T_IsDistributiveLattice_420 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_456 :: T_IsDistributiveLattice_420
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_456 T_IsDistributiveLattice_420
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 ((T_IsDistributiveLattice_420 -> T_IsLattice_340)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_420 -> T_IsLattice_340
d_isLattice_430 (T_IsDistributiveLattice_420 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_420
v0))))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.x∧y≤x
d_x'8743'y'8804'x_458 ::
  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_420 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'x_458 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_420
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'x_458 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsDistributiveLattice_420
v8
  = T_IsDistributiveLattice_420 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_458 T_IsDistributiveLattice_420
v8
du_x'8743'y'8804'x_458 ::
  T_IsDistributiveLattice_420 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_458 :: T_IsDistributiveLattice_420 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_458 T_IsDistributiveLattice_420
v0
  = let v1 :: T_IsLattice_340
v1 = T_IsDistributiveLattice_420 -> T_IsLattice_340
d_isLattice_430 (T_IsDistributiveLattice_420 -> T_IsDistributiveLattice_420
forall a b. a -> b
coe T_IsDistributiveLattice_420
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_196 ((T_IsLattice_340 -> T_IsMeetSemilattice_180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsMeetSemilattice_180
du_isMeetSemilattice_360 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v1)))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.x∧y≤y
d_x'8743'y'8804'y_460 ::
  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_420 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'y_460 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_420
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'y_460 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsDistributiveLattice_420
v8
  = T_IsDistributiveLattice_420 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_460 T_IsDistributiveLattice_420
v8
du_x'8743'y'8804'y_460 ::
  T_IsDistributiveLattice_420 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_460 :: T_IsDistributiveLattice_420 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_460 T_IsDistributiveLattice_420
v0
  = let v1 :: T_IsLattice_340
v1 = T_IsDistributiveLattice_420 -> T_IsLattice_340
d_isLattice_430 (T_IsDistributiveLattice_420 -> T_IsDistributiveLattice_420
forall a b. a -> b
coe T_IsDistributiveLattice_420
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_208 ((T_IsLattice_340 -> T_IsMeetSemilattice_180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsMeetSemilattice_180
du_isMeetSemilattice_360 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v1)))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.x≤x∨y
d_x'8804'x'8744'y_462 ::
  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_420 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8804'x'8744'y_462 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_420
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8804'x'8744'y_462 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsDistributiveLattice_420
v8
  = T_IsDistributiveLattice_420 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_462 T_IsDistributiveLattice_420
v8
du_x'8804'x'8744'y_462 ::
  T_IsDistributiveLattice_420 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_462 :: T_IsDistributiveLattice_420 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_462 T_IsDistributiveLattice_420
v0
  = let v1 :: T_IsLattice_340
v1 = T_IsDistributiveLattice_420 -> T_IsLattice_340
d_isLattice_430 (T_IsDistributiveLattice_420 -> T_IsDistributiveLattice_420
forall a b. a -> b
coe T_IsDistributiveLattice_420
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_38 ((T_IsLattice_340 -> T_IsJoinSemilattice_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_358 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v1)))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.y≤x∨y
d_y'8804'x'8744'y_464 ::
  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_420 -> AgdaAny -> AgdaAny -> AgdaAny
d_y'8804'x'8744'y_464 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_420
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_y'8804'x'8744'y_464 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsDistributiveLattice_420
v8
  = T_IsDistributiveLattice_420 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_464 T_IsDistributiveLattice_420
v8
du_y'8804'x'8744'y_464 ::
  T_IsDistributiveLattice_420 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_464 :: T_IsDistributiveLattice_420 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_464 T_IsDistributiveLattice_420
v0
  = let v1 :: T_IsLattice_340
v1 = T_IsDistributiveLattice_420 -> T_IsLattice_340
d_isLattice_430 (T_IsDistributiveLattice_420 -> T_IsDistributiveLattice_420
forall a b. a -> b
coe T_IsDistributiveLattice_420
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_50 ((T_IsLattice_340 -> T_IsJoinSemilattice_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_358 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v1)))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.∧-greatest
d_'8743''45'greatest_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) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_420 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'greatest_466 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_420
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'greatest_466 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsDistributiveLattice_420
v8
  = T_IsDistributiveLattice_420
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_466 T_IsDistributiveLattice_420
v8
du_'8743''45'greatest_466 ::
  T_IsDistributiveLattice_420 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_466 :: T_IsDistributiveLattice_420
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_466 T_IsDistributiveLattice_420
v0
  = let v1 :: T_IsLattice_340
v1 = T_IsDistributiveLattice_420 -> T_IsLattice_340
d_isLattice_430 (T_IsDistributiveLattice_420 -> T_IsDistributiveLattice_420
forall a b. a -> b
coe T_IsDistributiveLattice_420
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMeetSemilattice_180
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMeetSemilattice_180
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_222 ((T_IsLattice_340 -> T_IsMeetSemilattice_180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsMeetSemilattice_180
du_isMeetSemilattice_360 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v1)))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.∨-least
d_'8744''45'least_468 ::
  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_420 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'least_468 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_420
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'least_468 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsDistributiveLattice_420
v8
  = T_IsDistributiveLattice_420
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_468 T_IsDistributiveLattice_420
v8
du_'8744''45'least_468 ::
  T_IsDistributiveLattice_420 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_468 :: T_IsDistributiveLattice_420
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_468 T_IsDistributiveLattice_420
v0
  = let v1 :: T_IsLattice_340
v1 = T_IsDistributiveLattice_420 -> T_IsLattice_340
d_isLattice_430 (T_IsDistributiveLattice_420 -> T_IsDistributiveLattice_420
forall a b. a -> b
coe T_IsDistributiveLattice_420
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsJoinSemilattice_22
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_64 ((T_IsLattice_340 -> T_IsJoinSemilattice_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_358 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v1)))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.∼-resp-≈
d_'8764''45'resp'45''8776'_470 ::
  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_420 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_470 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_420
-> T_Σ_14
d_'8764''45'resp'45''8776'_470 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsDistributiveLattice_420
v8
  = T_IsDistributiveLattice_420 -> T_Σ_14
du_'8764''45'resp'45''8776'_470 T_IsDistributiveLattice_420
v8
du_'8764''45'resp'45''8776'_470 ::
  T_IsDistributiveLattice_420 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_470 :: T_IsDistributiveLattice_420 -> T_Σ_14
du_'8764''45'resp'45''8776'_470 T_IsDistributiveLattice_420
v0
  = let v1 :: T_IsLattice_340
v1 = T_IsDistributiveLattice_420 -> T_IsLattice_340
d_isLattice_430 (T_IsDistributiveLattice_420 -> T_IsDistributiveLattice_420
forall a b. a -> b
coe T_IsDistributiveLattice_420
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
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'_118
            ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_472 ::
  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_420 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_472 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_420
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_472 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7
                                    T_IsDistributiveLattice_420
v8
  = T_IsDistributiveLattice_420
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_472 T_IsDistributiveLattice_420
v8
du_'8764''45'resp'691''45''8776'_472 ::
  T_IsDistributiveLattice_420 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_472 :: T_IsDistributiveLattice_420
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_472 T_IsDistributiveLattice_420
v0
  = let v1 :: T_IsLattice_340
v1 = T_IsDistributiveLattice_420 -> T_IsLattice_340
d_isLattice_430 (T_IsDistributiveLattice_420 -> T_IsDistributiveLattice_420
forall a b. a -> b
coe T_IsDistributiveLattice_420
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
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'_116
            ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_474 ::
  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_420 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_474 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_420
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_474 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7
                                    T_IsDistributiveLattice_420
v8
  = T_IsDistributiveLattice_420
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_474 T_IsDistributiveLattice_420
v8
du_'8764''45'resp'737''45''8776'_474 ::
  T_IsDistributiveLattice_420 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_474 :: T_IsDistributiveLattice_420
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_474 T_IsDistributiveLattice_420
v0
  = let v1 :: T_IsLattice_340
v1 = T_IsDistributiveLattice_420 -> T_IsLattice_340
d_isLattice_430 (T_IsDistributiveLattice_420 -> T_IsDistributiveLattice_420
forall a b. a -> b
coe T_IsDistributiveLattice_420
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
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'_114
            ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.≲-resp-≈
d_'8818''45'resp'45''8776'_476 ::
  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_420 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8818''45'resp'45''8776'_476 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_420
-> T_Σ_14
d_'8818''45'resp'45''8776'_476 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsDistributiveLattice_420
v8
  = T_IsDistributiveLattice_420 -> T_Σ_14
du_'8818''45'resp'45''8776'_476 T_IsDistributiveLattice_420
v8
du_'8818''45'resp'45''8776'_476 ::
  T_IsDistributiveLattice_420 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8818''45'resp'45''8776'_476 :: T_IsDistributiveLattice_420 -> T_Σ_14
du_'8818''45'resp'45''8776'_476 T_IsDistributiveLattice_420
v0
  = let v1 :: T_IsLattice_340
v1 = T_IsDistributiveLattice_420 -> T_IsLattice_340
d_isLattice_430 (T_IsDistributiveLattice_420 -> T_IsDistributiveLattice_420
forall a b. a -> b
coe T_IsDistributiveLattice_420
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
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_'8818''45'resp'45''8776'_112
            ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.≲-respʳ-≈
d_'8818''45'resp'691''45''8776'_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) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  T_IsDistributiveLattice_420 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'691''45''8776'_478 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_420
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'691''45''8776'_478 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7
                                    T_IsDistributiveLattice_420
v8
  = T_IsDistributiveLattice_420
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_478 T_IsDistributiveLattice_420
v8
du_'8818''45'resp'691''45''8776'_478 ::
  T_IsDistributiveLattice_420 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_478 :: T_IsDistributiveLattice_420
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_478 T_IsDistributiveLattice_420
v0
  = let v1 :: T_IsLattice_340
v1 = T_IsDistributiveLattice_420 -> T_IsLattice_340
d_isLattice_430 (T_IsDistributiveLattice_420 -> T_IsDistributiveLattice_420
forall a b. a -> b
coe T_IsDistributiveLattice_420
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
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_'8818''45'resp'691''45''8776'_106
            ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.≲-respˡ-≈
d_'8818''45'resp'737''45''8776'_480 ::
  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_420 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'737''45''8776'_480 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_420
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'737''45''8776'_480 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7
                                    T_IsDistributiveLattice_420
v8
  = T_IsDistributiveLattice_420
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_480 T_IsDistributiveLattice_420
v8
du_'8818''45'resp'737''45''8776'_480 ::
  T_IsDistributiveLattice_420 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_480 :: T_IsDistributiveLattice_420
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_480 T_IsDistributiveLattice_420
v0
  = let v1 :: T_IsLattice_340
v1 = T_IsDistributiveLattice_420 -> T_IsLattice_340
d_isLattice_430 (T_IsDistributiveLattice_420 -> T_IsDistributiveLattice_420
forall a b. a -> b
coe T_IsDistributiveLattice_420
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
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_'8818''45'resp'737''45''8776'_100
            ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.Eq.isPartialEquivalence
d_isPartialEquivalence_484 ::
  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_420 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_484 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_420
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_484 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsDistributiveLattice_420
v8
  = T_IsDistributiveLattice_420 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_484 T_IsDistributiveLattice_420
v8
du_isPartialEquivalence_484 ::
  T_IsDistributiveLattice_420 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_484 :: T_IsDistributiveLattice_420 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_484 T_IsDistributiveLattice_420
v0
  = let v1 :: T_IsLattice_340
v1 = T_IsDistributiveLattice_420 -> T_IsLattice_340
d_isLattice_430 (T_IsDistributiveLattice_420 -> T_IsDistributiveLattice_420
forall a b. a -> b
coe T_IsDistributiveLattice_420
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreorder_70
v3
                = T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                    (T_IsPartialOrder_174 -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsPartialOrder_174
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.Structures.IsDistributiveLattice._.Eq.refl
d_refl_486 :: T_IsDistributiveLattice_420 -> AgdaAny -> AgdaAny
d_refl_486 :: T_IsDistributiveLattice_420 -> AgdaAny -> AgdaAny
d_refl_486 T_IsDistributiveLattice_420
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 ((T_IsDistributiveLattice_420 -> T_IsLattice_340)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_420 -> T_IsLattice_340
d_isLattice_430 (T_IsDistributiveLattice_420 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_420
v0)))))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.Eq.reflexive
d_reflexive_488 ::
  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_420 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_488 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_420
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_488 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsDistributiveLattice_420
v8
  = T_IsDistributiveLattice_420
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_488 T_IsDistributiveLattice_420
v8
du_reflexive_488 ::
  T_IsDistributiveLattice_420 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_488 :: T_IsDistributiveLattice_420
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_488 T_IsDistributiveLattice_420
v0
  = let v1 :: T_IsLattice_340
v1 = T_IsDistributiveLattice_420 -> T_IsLattice_340
d_isLattice_430 (T_IsDistributiveLattice_420 -> T_IsDistributiveLattice_420
forall a b. a -> b
coe T_IsDistributiveLattice_420
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreorder_70
v3
                = T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                    (T_IsPartialOrder_174 -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsPartialOrder_174
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.Structures.IsDistributiveLattice._.Eq.sym
d_sym_490 ::
  T_IsDistributiveLattice_420 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_490 :: T_IsDistributiveLattice_420
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_490 T_IsDistributiveLattice_420
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 ((T_IsDistributiveLattice_420 -> T_IsLattice_340)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_420 -> T_IsLattice_340
d_isLattice_430 (T_IsDistributiveLattice_420 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_420
v0)))))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.Eq.trans
d_trans_492 ::
  T_IsDistributiveLattice_420 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_492 :: T_IsDistributiveLattice_420
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_492 T_IsDistributiveLattice_420
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 ((T_IsDistributiveLattice_420 -> T_IsLattice_340)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_420 -> T_IsLattice_340
d_isLattice_430 (T_IsDistributiveLattice_420 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_420
v0)))))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice
d_IsBoundedLattice_502 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsBoundedLattice_502 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 p
a9 = ()
data T_IsBoundedLattice_502
  = C_IsBoundedLattice'46'constructor_21319 T_IsLattice_340
                                            (AgdaAny -> AgdaAny) (AgdaAny -> AgdaAny)
-- Relation.Binary.Lattice.Structures.IsBoundedLattice.isLattice
d_isLattice_518 :: T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 :: T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 T_IsBoundedLattice_502
v0
  = case T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v0 of
      C_IsBoundedLattice'46'constructor_21319 T_IsLattice_340
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 -> T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
v1
      T_IsBoundedLattice_502
_ -> T_IsLattice_340
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.Structures.IsBoundedLattice.maximum
d_maximum_520 :: T_IsBoundedLattice_502 -> AgdaAny -> AgdaAny
d_maximum_520 :: T_IsBoundedLattice_502 -> AgdaAny -> AgdaAny
d_maximum_520 T_IsBoundedLattice_502
v0
  = case T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v0 of
      C_IsBoundedLattice'46'constructor_21319 T_IsLattice_340
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_IsBoundedLattice_502
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.Structures.IsBoundedLattice.minimum
d_minimum_522 :: T_IsBoundedLattice_502 -> AgdaAny -> AgdaAny
d_minimum_522 :: T_IsBoundedLattice_502 -> AgdaAny -> AgdaAny
d_minimum_522 T_IsBoundedLattice_502
v0
  = case T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v0 of
      C_IsBoundedLattice'46'constructor_21319 T_IsLattice_340
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v3
      T_IsBoundedLattice_502
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.antisym
d_antisym_526 ::
  T_IsBoundedLattice_502 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_526 :: T_IsBoundedLattice_502
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_526 T_IsBoundedLattice_502
v0
  = (T_IsPartialOrder_174
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_174
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_184
      ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502
v0)))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.infimum
d_infimum_528 ::
  T_IsBoundedLattice_502 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_infimum_528 :: T_IsBoundedLattice_502 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_528 T_IsBoundedLattice_502
v0 = (T_IsLattice_340 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsLattice_340 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_356 ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502
v0))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.isEquivalence
d_isEquivalence_530 ::
  T_IsBoundedLattice_502 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_530 :: T_IsBoundedLattice_502 -> T_IsEquivalence_26
d_isEquivalence_530 T_IsBoundedLattice_502
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502
v0))))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.isJoinSemilattice
d_isJoinSemilattice_532 ::
  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_502 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_532 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_502
-> T_IsJoinSemilattice_22
d_isJoinSemilattice_532 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny
v8 ~AgdaAny
v9 T_IsBoundedLattice_502
v10
  = T_IsBoundedLattice_502 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_532 T_IsBoundedLattice_502
v10
du_isJoinSemilattice_532 ::
  T_IsBoundedLattice_502 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_532 :: T_IsBoundedLattice_502 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_532 T_IsBoundedLattice_502
v0
  = (T_IsLattice_340 -> T_IsJoinSemilattice_22)
-> AgdaAny -> T_IsJoinSemilattice_22
forall a b. a -> b
coe T_IsLattice_340 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_358 ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502
v0))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.isMeetSemilattice
d_isMeetSemilattice_534 ::
  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_502 -> T_IsMeetSemilattice_180
d_isMeetSemilattice_534 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_502
-> T_IsMeetSemilattice_180
d_isMeetSemilattice_534 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny
v8 ~AgdaAny
v9 T_IsBoundedLattice_502
v10
  = T_IsBoundedLattice_502 -> T_IsMeetSemilattice_180
du_isMeetSemilattice_534 T_IsBoundedLattice_502
v10
du_isMeetSemilattice_534 ::
  T_IsBoundedLattice_502 -> T_IsMeetSemilattice_180
du_isMeetSemilattice_534 :: T_IsBoundedLattice_502 -> T_IsMeetSemilattice_180
du_isMeetSemilattice_534 T_IsBoundedLattice_502
v0
  = (T_IsLattice_340 -> T_IsMeetSemilattice_180)
-> AgdaAny -> T_IsMeetSemilattice_180
forall a b. a -> b
coe T_IsLattice_340 -> T_IsMeetSemilattice_180
du_isMeetSemilattice_360 ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502
v0))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.isPartialOrder
d_isPartialOrder_536 ::
  T_IsBoundedLattice_502 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_174
d_isPartialOrder_536 :: T_IsBoundedLattice_502 -> T_IsPartialOrder_174
d_isPartialOrder_536 T_IsBoundedLattice_502
v0
  = (T_IsLattice_340 -> T_IsPartialOrder_174)
-> AgdaAny -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502
v0))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.isPreorder
d_isPreorder_538 ::
  T_IsBoundedLattice_502 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_538 :: T_IsBoundedLattice_502 -> T_IsPreorder_70
d_isPreorder_538 T_IsBoundedLattice_502
v0
  = (T_IsPartialOrder_174 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
      ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502
v0)))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.refl
d_refl_540 ::
  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_502 -> AgdaAny -> AgdaAny
d_refl_540 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_502
-> AgdaAny
-> AgdaAny
d_refl_540 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny
v8 ~AgdaAny
v9 T_IsBoundedLattice_502
v10
  = T_IsBoundedLattice_502 -> AgdaAny -> AgdaAny
du_refl_540 T_IsBoundedLattice_502
v10
du_refl_540 :: T_IsBoundedLattice_502 -> AgdaAny -> AgdaAny
du_refl_540 :: T_IsBoundedLattice_502 -> AgdaAny -> AgdaAny
du_refl_540 T_IsBoundedLattice_502
v0
  = let v1 :: T_IsLattice_340
v1 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.reflexive
d_reflexive_542 ::
  T_IsBoundedLattice_502 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_542 :: T_IsBoundedLattice_502 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_542 T_IsBoundedLattice_502
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502
v0))))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.supremum
d_supremum_544 ::
  T_IsBoundedLattice_502 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_supremum_544 :: T_IsBoundedLattice_502 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_544 T_IsBoundedLattice_502
v0
  = (T_IsLattice_340 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsLattice_340 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_354 ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502
v0))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.trans
d_trans_546 ::
  T_IsBoundedLattice_502 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_546 :: T_IsBoundedLattice_502
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_546 T_IsBoundedLattice_502
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502
v0))))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.x∧y≤x
d_x'8743'y'8804'x_548 ::
  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_502 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'x_548 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_502
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'x_548 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny
v8 ~AgdaAny
v9 T_IsBoundedLattice_502
v10
  = T_IsBoundedLattice_502 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_548 T_IsBoundedLattice_502
v10
du_x'8743'y'8804'x_548 ::
  T_IsBoundedLattice_502 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_548 :: T_IsBoundedLattice_502 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_548 T_IsBoundedLattice_502
v0
  = let v1 :: T_IsLattice_340
v1 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_196 ((T_IsLattice_340 -> T_IsMeetSemilattice_180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsMeetSemilattice_180
du_isMeetSemilattice_360 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v1)))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.x∧y≤y
d_x'8743'y'8804'y_550 ::
  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_502 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'y_550 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_502
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'y_550 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny
v8 ~AgdaAny
v9 T_IsBoundedLattice_502
v10
  = T_IsBoundedLattice_502 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_550 T_IsBoundedLattice_502
v10
du_x'8743'y'8804'y_550 ::
  T_IsBoundedLattice_502 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_550 :: T_IsBoundedLattice_502 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_550 T_IsBoundedLattice_502
v0
  = let v1 :: T_IsLattice_340
v1 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_208 ((T_IsLattice_340 -> T_IsMeetSemilattice_180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsMeetSemilattice_180
du_isMeetSemilattice_360 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v1)))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.x≤x∨y
d_x'8804'x'8744'y_552 ::
  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_502 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8804'x'8744'y_552 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_502
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8804'x'8744'y_552 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny
v8 ~AgdaAny
v9 T_IsBoundedLattice_502
v10
  = T_IsBoundedLattice_502 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_552 T_IsBoundedLattice_502
v10
du_x'8804'x'8744'y_552 ::
  T_IsBoundedLattice_502 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_552 :: T_IsBoundedLattice_502 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_552 T_IsBoundedLattice_502
v0
  = let v1 :: T_IsLattice_340
v1 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_38 ((T_IsLattice_340 -> T_IsJoinSemilattice_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_358 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v1)))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.y≤x∨y
d_y'8804'x'8744'y_554 ::
  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_502 -> AgdaAny -> AgdaAny -> AgdaAny
d_y'8804'x'8744'y_554 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_502
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_y'8804'x'8744'y_554 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny
v8 ~AgdaAny
v9 T_IsBoundedLattice_502
v10
  = T_IsBoundedLattice_502 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_554 T_IsBoundedLattice_502
v10
du_y'8804'x'8744'y_554 ::
  T_IsBoundedLattice_502 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_554 :: T_IsBoundedLattice_502 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_554 T_IsBoundedLattice_502
v0
  = let v1 :: T_IsLattice_340
v1 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_50 ((T_IsLattice_340 -> T_IsJoinSemilattice_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_358 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v1)))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.∧-greatest
d_'8743''45'greatest_556 ::
  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_502 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'greatest_556 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_502
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'greatest_556 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny
v8 ~AgdaAny
v9
                         T_IsBoundedLattice_502
v10
  = T_IsBoundedLattice_502
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_556 T_IsBoundedLattice_502
v10
du_'8743''45'greatest_556 ::
  T_IsBoundedLattice_502 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_556 :: T_IsBoundedLattice_502
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_556 T_IsBoundedLattice_502
v0
  = let v1 :: T_IsLattice_340
v1 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMeetSemilattice_180
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMeetSemilattice_180
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_222 ((T_IsLattice_340 -> T_IsMeetSemilattice_180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsMeetSemilattice_180
du_isMeetSemilattice_360 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v1)))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.∨-least
d_'8744''45'least_558 ::
  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_502 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'least_558 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_502
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'least_558 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny
v8 ~AgdaAny
v9 T_IsBoundedLattice_502
v10
  = T_IsBoundedLattice_502
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_558 T_IsBoundedLattice_502
v10
du_'8744''45'least_558 ::
  T_IsBoundedLattice_502 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_558 :: T_IsBoundedLattice_502
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_558 T_IsBoundedLattice_502
v0
  = let v1 :: T_IsLattice_340
v1 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsJoinSemilattice_22
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_64 ((T_IsLattice_340 -> T_IsJoinSemilattice_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_358 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v1)))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.∼-resp-≈
d_'8764''45'resp'45''8776'_560 ::
  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_502 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_560 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_502
-> T_Σ_14
d_'8764''45'resp'45''8776'_560 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny
v8
                               ~AgdaAny
v9 T_IsBoundedLattice_502
v10
  = T_IsBoundedLattice_502 -> T_Σ_14
du_'8764''45'resp'45''8776'_560 T_IsBoundedLattice_502
v10
du_'8764''45'resp'45''8776'_560 ::
  T_IsBoundedLattice_502 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_560 :: T_IsBoundedLattice_502 -> T_Σ_14
du_'8764''45'resp'45''8776'_560 T_IsBoundedLattice_502
v0
  = let v1 :: T_IsLattice_340
v1 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
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'_118
            ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_562 ::
  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_502 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_562 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_502
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_562 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7
                                    ~AgdaAny
v8 ~AgdaAny
v9 T_IsBoundedLattice_502
v10
  = T_IsBoundedLattice_502
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_562 T_IsBoundedLattice_502
v10
du_'8764''45'resp'691''45''8776'_562 ::
  T_IsBoundedLattice_502 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_562 :: T_IsBoundedLattice_502
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_562 T_IsBoundedLattice_502
v0
  = let v1 :: T_IsLattice_340
v1 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
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'_116
            ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_564 ::
  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_502 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_564 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_502
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_564 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7
                                    ~AgdaAny
v8 ~AgdaAny
v9 T_IsBoundedLattice_502
v10
  = T_IsBoundedLattice_502
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_564 T_IsBoundedLattice_502
v10
du_'8764''45'resp'737''45''8776'_564 ::
  T_IsBoundedLattice_502 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_564 :: T_IsBoundedLattice_502
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_564 T_IsBoundedLattice_502
v0
  = let v1 :: T_IsLattice_340
v1 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
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'_114
            ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.≲-resp-≈
d_'8818''45'resp'45''8776'_566 ::
  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_502 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8818''45'resp'45''8776'_566 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_502
-> T_Σ_14
d_'8818''45'resp'45''8776'_566 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny
v8
                               ~AgdaAny
v9 T_IsBoundedLattice_502
v10
  = T_IsBoundedLattice_502 -> T_Σ_14
du_'8818''45'resp'45''8776'_566 T_IsBoundedLattice_502
v10
du_'8818''45'resp'45''8776'_566 ::
  T_IsBoundedLattice_502 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8818''45'resp'45''8776'_566 :: T_IsBoundedLattice_502 -> T_Σ_14
du_'8818''45'resp'45''8776'_566 T_IsBoundedLattice_502
v0
  = let v1 :: T_IsLattice_340
v1 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
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_'8818''45'resp'45''8776'_112
            ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.≲-respʳ-≈
d_'8818''45'resp'691''45''8776'_568 ::
  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_502 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'691''45''8776'_568 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_502
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'691''45''8776'_568 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7
                                    ~AgdaAny
v8 ~AgdaAny
v9 T_IsBoundedLattice_502
v10
  = T_IsBoundedLattice_502
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_568 T_IsBoundedLattice_502
v10
du_'8818''45'resp'691''45''8776'_568 ::
  T_IsBoundedLattice_502 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_568 :: T_IsBoundedLattice_502
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_568 T_IsBoundedLattice_502
v0
  = let v1 :: T_IsLattice_340
v1 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
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_'8818''45'resp'691''45''8776'_106
            ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.≲-respˡ-≈
d_'8818''45'resp'737''45''8776'_570 ::
  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_502 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'737''45''8776'_570 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_502
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'737''45''8776'_570 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7
                                    ~AgdaAny
v8 ~AgdaAny
v9 T_IsBoundedLattice_502
v10
  = T_IsBoundedLattice_502
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_570 T_IsBoundedLattice_502
v10
du_'8818''45'resp'737''45''8776'_570 ::
  T_IsBoundedLattice_502 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_570 :: T_IsBoundedLattice_502
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_570 T_IsBoundedLattice_502
v0
  = let v1 :: T_IsLattice_340
v1 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
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_'8818''45'resp'737''45''8776'_100
            ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
               (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.Eq.isPartialEquivalence
d_isPartialEquivalence_574 ::
  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_502 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_574 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_502
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_574 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny
v8 ~AgdaAny
v9
                           T_IsBoundedLattice_502
v10
  = T_IsBoundedLattice_502 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_574 T_IsBoundedLattice_502
v10
du_isPartialEquivalence_574 ::
  T_IsBoundedLattice_502 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_574 :: T_IsBoundedLattice_502 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_574 T_IsBoundedLattice_502
v0
  = let v1 :: T_IsLattice_340
v1 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreorder_70
v3
                = T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                    (T_IsPartialOrder_174 -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsPartialOrder_174
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.Structures.IsBoundedLattice._.Eq.refl
d_refl_576 :: T_IsBoundedLattice_502 -> AgdaAny -> AgdaAny
d_refl_576 :: T_IsBoundedLattice_502 -> AgdaAny -> AgdaAny
d_refl_576 T_IsBoundedLattice_502
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502
v0)))))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.Eq.reflexive
d_reflexive_578 ::
  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_502 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_578 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_502
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_578 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny
v8 ~AgdaAny
v9 T_IsBoundedLattice_502
v10
  = T_IsBoundedLattice_502
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_578 T_IsBoundedLattice_502
v10
du_reflexive_578 ::
  T_IsBoundedLattice_502 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_578 :: T_IsBoundedLattice_502
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_578 T_IsBoundedLattice_502
v0
  = let v1 :: T_IsLattice_340
v1 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_174
v2 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreorder_70
v3
                = T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                    (T_IsPartialOrder_174 -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsPartialOrder_174
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.Structures.IsBoundedLattice._.Eq.sym
d_sym_580 ::
  T_IsBoundedLattice_502 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_580 :: T_IsBoundedLattice_502 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_580 T_IsBoundedLattice_502
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502
v0)))))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.Eq.trans
d_trans_582 ::
  T_IsBoundedLattice_502 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_582 :: T_IsBoundedLattice_502
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_582 T_IsBoundedLattice_502
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502
v0)))))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice.isBoundedJoinSemilattice
d_isBoundedJoinSemilattice_584 ::
  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_502 -> T_IsBoundedJoinSemilattice_116
d_isBoundedJoinSemilattice_584 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_502
-> T_IsBoundedJoinSemilattice_116
d_isBoundedJoinSemilattice_584 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny
v8
                               ~AgdaAny
v9 T_IsBoundedLattice_502
v10
  = T_IsBoundedLattice_502 -> T_IsBoundedJoinSemilattice_116
du_isBoundedJoinSemilattice_584 T_IsBoundedLattice_502
v10
du_isBoundedJoinSemilattice_584 ::
  T_IsBoundedLattice_502 -> T_IsBoundedJoinSemilattice_116
du_isBoundedJoinSemilattice_584 :: T_IsBoundedLattice_502 -> T_IsBoundedJoinSemilattice_116
du_isBoundedJoinSemilattice_584 T_IsBoundedLattice_502
v0
  = (T_IsJoinSemilattice_22
 -> (AgdaAny -> AgdaAny) -> T_IsBoundedJoinSemilattice_116)
-> AgdaAny -> AgdaAny -> T_IsBoundedJoinSemilattice_116
forall a b. a -> b
coe
      T_IsJoinSemilattice_22
-> (AgdaAny -> AgdaAny) -> T_IsBoundedJoinSemilattice_116
C_IsBoundedJoinSemilattice'46'constructor_5215
      ((T_IsLattice_340 -> T_IsJoinSemilattice_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_358 ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502
v0)))
      ((T_IsBoundedLattice_502 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502 -> AgdaAny -> AgdaAny
d_minimum_522 (T_IsBoundedLattice_502 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502
v0))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice.isBoundedMeetSemilattice
d_isBoundedMeetSemilattice_586 ::
  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_502 -> T_IsBoundedMeetSemilattice_274
d_isBoundedMeetSemilattice_586 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_502
-> T_IsBoundedMeetSemilattice_274
d_isBoundedMeetSemilattice_586 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny
v8
                               ~AgdaAny
v9 T_IsBoundedLattice_502
v10
  = T_IsBoundedLattice_502 -> T_IsBoundedMeetSemilattice_274
du_isBoundedMeetSemilattice_586 T_IsBoundedLattice_502
v10
du_isBoundedMeetSemilattice_586 ::
  T_IsBoundedLattice_502 -> T_IsBoundedMeetSemilattice_274
du_isBoundedMeetSemilattice_586 :: T_IsBoundedLattice_502 -> T_IsBoundedMeetSemilattice_274
du_isBoundedMeetSemilattice_586 T_IsBoundedLattice_502
v0
  = (T_IsMeetSemilattice_180
 -> (AgdaAny -> AgdaAny) -> T_IsBoundedMeetSemilattice_274)
-> AgdaAny -> AgdaAny -> T_IsBoundedMeetSemilattice_274
forall a b. a -> b
coe
      T_IsMeetSemilattice_180
-> (AgdaAny -> AgdaAny) -> T_IsBoundedMeetSemilattice_274
C_IsBoundedMeetSemilattice'46'constructor_12265
      ((T_IsLattice_340 -> T_IsMeetSemilattice_180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsMeetSemilattice_180
du_isMeetSemilattice_360 ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502
v0)))
      ((T_IsBoundedLattice_502 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502 -> AgdaAny -> AgdaAny
d_maximum_520 (T_IsBoundedLattice_502 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502
v0))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra
d_IsHeytingAlgebra_598 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsHeytingAlgebra_598 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_598
  = C_IsHeytingAlgebra'46'constructor_25303 T_IsBoundedLattice_502
                                            (AgdaAny ->
                                             AgdaAny ->
                                             AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14)
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra.isBoundedLattice
d_isBoundedLattice_614 ::
  T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 :: T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 T_IsHeytingAlgebra_598
v0
  = case T_IsHeytingAlgebra_598 -> T_IsHeytingAlgebra_598
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v0 of
      C_IsHeytingAlgebra'46'constructor_25303 T_IsBoundedLattice_502
v1 AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
v2 -> T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v1
      T_IsHeytingAlgebra_598
_ -> T_IsBoundedLattice_502
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra.exponential
d_exponential_616 ::
  T_IsHeytingAlgebra_598 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_exponential_616 :: T_IsHeytingAlgebra_598 -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
d_exponential_616 T_IsHeytingAlgebra_598
v0
  = case T_IsHeytingAlgebra_598 -> T_IsHeytingAlgebra_598
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v0 of
      C_IsHeytingAlgebra'46'constructor_25303 T_IsBoundedLattice_502
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_598
_ -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra.transpose-⇨
d_transpose'45''8680'_624 ::
  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_598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_transpose'45''8680'_624 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_598
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_transpose'45''8680'_624 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny -> AgdaAny
v8 ~AgdaAny
v9
                          ~AgdaAny
v10 T_IsHeytingAlgebra_598
v11 AgdaAny
v12 AgdaAny
v13 AgdaAny
v14
  = T_IsHeytingAlgebra_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8680'_624 T_IsHeytingAlgebra_598
v11 AgdaAny
v12 AgdaAny
v13 AgdaAny
v14
du_transpose'45''8680'_624 ::
  T_IsHeytingAlgebra_598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8680'_624 :: T_IsHeytingAlgebra_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8680'_624 T_IsHeytingAlgebra_598
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_598 -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14)
-> T_IsHeytingAlgebra_598
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598 -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
d_exponential_616 T_IsHeytingAlgebra_598
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3)
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra.transpose-∧
d_transpose'45''8743'_640 ::
  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_598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_transpose'45''8743'_640 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_598
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_transpose'45''8743'_640 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny -> AgdaAny
v8 ~AgdaAny
v9
                          ~AgdaAny
v10 T_IsHeytingAlgebra_598
v11 AgdaAny
v12 AgdaAny
v13 AgdaAny
v14
  = T_IsHeytingAlgebra_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8743'_640 T_IsHeytingAlgebra_598
v11 AgdaAny
v12 AgdaAny
v13 AgdaAny
v14
du_transpose'45''8743'_640 ::
  T_IsHeytingAlgebra_598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8743'_640 :: T_IsHeytingAlgebra_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8743'_640 T_IsHeytingAlgebra_598
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_598 -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14)
-> T_IsHeytingAlgebra_598
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598 -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
d_exponential_616 T_IsHeytingAlgebra_598
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3)
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.antisym
d_antisym_652 ::
  T_IsHeytingAlgebra_598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_652 :: T_IsHeytingAlgebra_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_652 T_IsHeytingAlgebra_598
v0
  = (T_IsPartialOrder_174
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_174
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_184
      ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352
         ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 ((T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v0))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.infimum
d_infimum_654 ::
  T_IsHeytingAlgebra_598 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_infimum_654 :: T_IsHeytingAlgebra_598 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_654 T_IsHeytingAlgebra_598
v0
  = (T_IsLattice_340 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsLattice_340 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_356
      ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 ((T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v0)))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.isBoundedJoinSemilattice
d_isBoundedJoinSemilattice_656 ::
  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_598 -> T_IsBoundedJoinSemilattice_116
d_isBoundedJoinSemilattice_656 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_598
-> T_IsBoundedJoinSemilattice_116
d_isBoundedJoinSemilattice_656 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny -> AgdaAny
v8
                               ~AgdaAny
v9 ~AgdaAny
v10 T_IsHeytingAlgebra_598
v11
  = T_IsHeytingAlgebra_598 -> T_IsBoundedJoinSemilattice_116
du_isBoundedJoinSemilattice_656 T_IsHeytingAlgebra_598
v11
du_isBoundedJoinSemilattice_656 ::
  T_IsHeytingAlgebra_598 -> T_IsBoundedJoinSemilattice_116
du_isBoundedJoinSemilattice_656 :: T_IsHeytingAlgebra_598 -> T_IsBoundedJoinSemilattice_116
du_isBoundedJoinSemilattice_656 T_IsHeytingAlgebra_598
v0
  = (T_IsBoundedLattice_502 -> T_IsBoundedJoinSemilattice_116)
-> AgdaAny -> T_IsBoundedJoinSemilattice_116
forall a b. a -> b
coe
      T_IsBoundedLattice_502 -> T_IsBoundedJoinSemilattice_116
du_isBoundedJoinSemilattice_584
      ((T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v0))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.isBoundedMeetSemilattice
d_isBoundedMeetSemilattice_658 ::
  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_598 -> T_IsBoundedMeetSemilattice_274
d_isBoundedMeetSemilattice_658 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_598
-> T_IsBoundedMeetSemilattice_274
d_isBoundedMeetSemilattice_658 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny -> AgdaAny
v8
                               ~AgdaAny
v9 ~AgdaAny
v10 T_IsHeytingAlgebra_598
v11
  = T_IsHeytingAlgebra_598 -> T_IsBoundedMeetSemilattice_274
du_isBoundedMeetSemilattice_658 T_IsHeytingAlgebra_598
v11
du_isBoundedMeetSemilattice_658 ::
  T_IsHeytingAlgebra_598 -> T_IsBoundedMeetSemilattice_274
du_isBoundedMeetSemilattice_658 :: T_IsHeytingAlgebra_598 -> T_IsBoundedMeetSemilattice_274
du_isBoundedMeetSemilattice_658 T_IsHeytingAlgebra_598
v0
  = (T_IsBoundedLattice_502 -> T_IsBoundedMeetSemilattice_274)
-> AgdaAny -> T_IsBoundedMeetSemilattice_274
forall a b. a -> b
coe
      T_IsBoundedLattice_502 -> T_IsBoundedMeetSemilattice_274
du_isBoundedMeetSemilattice_586
      ((T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v0))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.isEquivalence
d_isEquivalence_660 ::
  T_IsHeytingAlgebra_598 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_660 :: T_IsHeytingAlgebra_598 -> T_IsEquivalence_26
d_isEquivalence_660 T_IsHeytingAlgebra_598
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352
            ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 ((T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v0)))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.isJoinSemilattice
d_isJoinSemilattice_662 ::
  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_598 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_662 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_598
-> T_IsJoinSemilattice_22
d_isJoinSemilattice_662 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny -> AgdaAny
v8 ~AgdaAny
v9
                        ~AgdaAny
v10 T_IsHeytingAlgebra_598
v11
  = T_IsHeytingAlgebra_598 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_662 T_IsHeytingAlgebra_598
v11
du_isJoinSemilattice_662 ::
  T_IsHeytingAlgebra_598 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_662 :: T_IsHeytingAlgebra_598 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_662 T_IsHeytingAlgebra_598
v0
  = let v1 :: T_IsBoundedLattice_502
v1 = T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> T_IsHeytingAlgebra_598
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v0) in
    AgdaAny -> T_IsJoinSemilattice_22
forall a b. a -> b
coe ((T_IsLattice_340 -> T_IsJoinSemilattice_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_358 ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502
v1)))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.isLattice
d_isLattice_664 :: T_IsHeytingAlgebra_598 -> T_IsLattice_340
d_isLattice_664 :: T_IsHeytingAlgebra_598 -> T_IsLattice_340
d_isLattice_664 T_IsHeytingAlgebra_598
v0
  = (T_IsBoundedLattice_502 -> T_IsLattice_340)
-> AgdaAny -> T_IsLattice_340
forall a b. a -> b
coe T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 ((T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v0))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.isMeetSemilattice
d_isMeetSemilattice_666 ::
  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_598 -> T_IsMeetSemilattice_180
d_isMeetSemilattice_666 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_598
-> T_IsMeetSemilattice_180
d_isMeetSemilattice_666 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny -> AgdaAny
v8 ~AgdaAny
v9
                        ~AgdaAny
v10 T_IsHeytingAlgebra_598
v11
  = T_IsHeytingAlgebra_598 -> T_IsMeetSemilattice_180
du_isMeetSemilattice_666 T_IsHeytingAlgebra_598
v11
du_isMeetSemilattice_666 ::
  T_IsHeytingAlgebra_598 -> T_IsMeetSemilattice_180
du_isMeetSemilattice_666 :: T_IsHeytingAlgebra_598 -> T_IsMeetSemilattice_180
du_isMeetSemilattice_666 T_IsHeytingAlgebra_598
v0
  = let v1 :: T_IsBoundedLattice_502
v1 = T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> T_IsHeytingAlgebra_598
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v0) in
    AgdaAny -> T_IsMeetSemilattice_180
forall a b. a -> b
coe ((T_IsLattice_340 -> T_IsMeetSemilattice_180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsMeetSemilattice_180
du_isMeetSemilattice_360 ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502
v1)))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.isPartialOrder
d_isPartialOrder_668 ::
  T_IsHeytingAlgebra_598 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_174
d_isPartialOrder_668 :: T_IsHeytingAlgebra_598 -> T_IsPartialOrder_174
d_isPartialOrder_668 T_IsHeytingAlgebra_598
v0
  = (T_IsLattice_340 -> T_IsPartialOrder_174)
-> AgdaAny -> T_IsPartialOrder_174
forall a b. a -> b
coe
      T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352
      ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 ((T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v0)))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.isPreorder
d_isPreorder_670 ::
  T_IsHeytingAlgebra_598 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_670 :: T_IsHeytingAlgebra_598 -> T_IsPreorder_70
d_isPreorder_670 T_IsHeytingAlgebra_598
v0
  = (T_IsPartialOrder_174 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
      ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352
         ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 ((T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v0))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.maximum
d_maximum_672 :: T_IsHeytingAlgebra_598 -> AgdaAny -> AgdaAny
d_maximum_672 :: T_IsHeytingAlgebra_598 -> AgdaAny -> AgdaAny
d_maximum_672 T_IsHeytingAlgebra_598
v0
  = (T_IsBoundedLattice_502 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502 -> AgdaAny -> AgdaAny
d_maximum_520 ((T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v0))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.minimum
d_minimum_674 :: T_IsHeytingAlgebra_598 -> AgdaAny -> AgdaAny
d_minimum_674 :: T_IsHeytingAlgebra_598 -> AgdaAny -> AgdaAny
d_minimum_674 T_IsHeytingAlgebra_598
v0
  = (T_IsBoundedLattice_502 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502 -> AgdaAny -> AgdaAny
d_minimum_522 ((T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v0))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.refl
d_refl_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 -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> T_IsHeytingAlgebra_598 -> AgdaAny -> AgdaAny
d_refl_676 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_598
-> AgdaAny
-> AgdaAny
d_refl_676 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10 T_IsHeytingAlgebra_598
v11
  = T_IsHeytingAlgebra_598 -> AgdaAny -> AgdaAny
du_refl_676 T_IsHeytingAlgebra_598
v11
du_refl_676 :: T_IsHeytingAlgebra_598 -> AgdaAny -> AgdaAny
du_refl_676 :: T_IsHeytingAlgebra_598 -> AgdaAny -> AgdaAny
du_refl_676 T_IsHeytingAlgebra_598
v0
  = let v1 :: T_IsBoundedLattice_502
v1 = T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> T_IsHeytingAlgebra_598
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_340
v2 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_174
v3 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                  (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v3)))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.reflexive
d_reflexive_678 ::
  T_IsHeytingAlgebra_598 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_678 :: T_IsHeytingAlgebra_598 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_678 T_IsHeytingAlgebra_598
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352
            ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 ((T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v0)))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.supremum
d_supremum_680 ::
  T_IsHeytingAlgebra_598 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_supremum_680 :: T_IsHeytingAlgebra_598 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_680 T_IsHeytingAlgebra_598
v0
  = (T_IsLattice_340 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsLattice_340 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_354
      ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 ((T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v0)))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.trans
d_trans_682 ::
  T_IsHeytingAlgebra_598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_682 :: T_IsHeytingAlgebra_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_682 T_IsHeytingAlgebra_598
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352
            ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 ((T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v0)))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.x∧y≤x
d_x'8743'y'8804'x_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 -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsHeytingAlgebra_598 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'x_684 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_598
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'x_684 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10
                      T_IsHeytingAlgebra_598
v11
  = T_IsHeytingAlgebra_598 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_684 T_IsHeytingAlgebra_598
v11
du_x'8743'y'8804'x_684 ::
  T_IsHeytingAlgebra_598 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_684 :: T_IsHeytingAlgebra_598 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_684 T_IsHeytingAlgebra_598
v0
  = let v1 :: T_IsBoundedLattice_502
v1 = T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> T_IsHeytingAlgebra_598
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_340
v2 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_196 ((T_IsLattice_340 -> T_IsMeetSemilattice_180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsMeetSemilattice_180
du_isMeetSemilattice_360 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v2))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.x∧y≤y
d_x'8743'y'8804'y_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 -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsHeytingAlgebra_598 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'y_686 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_598
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'y_686 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10
                      T_IsHeytingAlgebra_598
v11
  = T_IsHeytingAlgebra_598 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_686 T_IsHeytingAlgebra_598
v11
du_x'8743'y'8804'y_686 ::
  T_IsHeytingAlgebra_598 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_686 :: T_IsHeytingAlgebra_598 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_686 T_IsHeytingAlgebra_598
v0
  = let v1 :: T_IsBoundedLattice_502
v1 = T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> T_IsHeytingAlgebra_598
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_340
v2 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_208 ((T_IsLattice_340 -> T_IsMeetSemilattice_180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsMeetSemilattice_180
du_isMeetSemilattice_360 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v2))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.x≤x∨y
d_x'8804'x'8744'y_688 ::
  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_598 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8804'x'8744'y_688 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_598
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8804'x'8744'y_688 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10
                      T_IsHeytingAlgebra_598
v11
  = T_IsHeytingAlgebra_598 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_688 T_IsHeytingAlgebra_598
v11
du_x'8804'x'8744'y_688 ::
  T_IsHeytingAlgebra_598 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_688 :: T_IsHeytingAlgebra_598 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_688 T_IsHeytingAlgebra_598
v0
  = let v1 :: T_IsBoundedLattice_502
v1 = T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> T_IsHeytingAlgebra_598
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_340
v2 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_38 ((T_IsLattice_340 -> T_IsJoinSemilattice_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_358 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v2))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.y≤x∨y
d_y'8804'x'8744'y_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 -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsHeytingAlgebra_598 -> AgdaAny -> AgdaAny -> AgdaAny
d_y'8804'x'8744'y_690 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_598
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_y'8804'x'8744'y_690 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10
                      T_IsHeytingAlgebra_598
v11
  = T_IsHeytingAlgebra_598 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_690 T_IsHeytingAlgebra_598
v11
du_y'8804'x'8744'y_690 ::
  T_IsHeytingAlgebra_598 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_690 :: T_IsHeytingAlgebra_598 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_690 T_IsHeytingAlgebra_598
v0
  = let v1 :: T_IsBoundedLattice_502
v1 = T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> T_IsHeytingAlgebra_598
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_340
v2 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_50 ((T_IsLattice_340 -> T_IsJoinSemilattice_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_358 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v2))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.∧-greatest
d_'8743''45'greatest_692 ::
  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_598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'greatest_692 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_598
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'greatest_692 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny -> AgdaAny
v8 ~AgdaAny
v9
                         ~AgdaAny
v10 T_IsHeytingAlgebra_598
v11
  = T_IsHeytingAlgebra_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_692 T_IsHeytingAlgebra_598
v11
du_'8743''45'greatest_692 ::
  T_IsHeytingAlgebra_598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_692 :: T_IsHeytingAlgebra_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_692 T_IsHeytingAlgebra_598
v0
  = let v1 :: T_IsBoundedLattice_502
v1 = T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> T_IsHeytingAlgebra_598
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_340
v2 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMeetSemilattice_180
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMeetSemilattice_180
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_222 ((T_IsLattice_340 -> T_IsMeetSemilattice_180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsMeetSemilattice_180
du_isMeetSemilattice_360 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v2))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.∨-least
d_'8744''45'least_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 -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsHeytingAlgebra_598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'least_694 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_598
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'least_694 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10
                      T_IsHeytingAlgebra_598
v11
  = T_IsHeytingAlgebra_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_694 T_IsHeytingAlgebra_598
v11
du_'8744''45'least_694 ::
  T_IsHeytingAlgebra_598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_694 :: T_IsHeytingAlgebra_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_694 T_IsHeytingAlgebra_598
v0
  = let v1 :: T_IsBoundedLattice_502
v1 = T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> T_IsHeytingAlgebra_598
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_340
v2 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsJoinSemilattice_22
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsJoinSemilattice_22
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_64 ((T_IsLattice_340 -> T_IsJoinSemilattice_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_358 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v2))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.∼-resp-≈
d_'8764''45'resp'45''8776'_696 ::
  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_598 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_696 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_598
-> T_Σ_14
d_'8764''45'resp'45''8776'_696 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny -> AgdaAny
v8
                               ~AgdaAny
v9 ~AgdaAny
v10 T_IsHeytingAlgebra_598
v11
  = T_IsHeytingAlgebra_598 -> T_Σ_14
du_'8764''45'resp'45''8776'_696 T_IsHeytingAlgebra_598
v11
du_'8764''45'resp'45''8776'_696 ::
  T_IsHeytingAlgebra_598 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_696 :: T_IsHeytingAlgebra_598 -> T_Σ_14
du_'8764''45'resp'45''8776'_696 T_IsHeytingAlgebra_598
v0
  = let v1 :: T_IsBoundedLattice_502
v1 = T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> T_IsHeytingAlgebra_598
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_340
v2 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_174
v3 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
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'_118
               ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                  (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v3)))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_698 ::
  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_598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_698 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_598
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_698 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7
                                    ~AgdaAny -> AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10 T_IsHeytingAlgebra_598
v11
  = T_IsHeytingAlgebra_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_698 T_IsHeytingAlgebra_598
v11
du_'8764''45'resp'691''45''8776'_698 ::
  T_IsHeytingAlgebra_598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_698 :: T_IsHeytingAlgebra_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_698 T_IsHeytingAlgebra_598
v0
  = let v1 :: T_IsBoundedLattice_502
v1 = T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> T_IsHeytingAlgebra_598
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_340
v2 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_174
v3 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
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'_116
               ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                  (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v3)))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_700 ::
  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_598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_700 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_598
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_700 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7
                                    ~AgdaAny -> AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10 T_IsHeytingAlgebra_598
v11
  = T_IsHeytingAlgebra_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_700 T_IsHeytingAlgebra_598
v11
du_'8764''45'resp'737''45''8776'_700 ::
  T_IsHeytingAlgebra_598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_700 :: T_IsHeytingAlgebra_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_700 T_IsHeytingAlgebra_598
v0
  = let v1 :: T_IsBoundedLattice_502
v1 = T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> T_IsHeytingAlgebra_598
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_340
v2 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_174
v3 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
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'_114
               ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                  (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v3)))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.≲-resp-≈
d_'8818''45'resp'45''8776'_702 ::
  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_598 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8818''45'resp'45''8776'_702 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_598
-> T_Σ_14
d_'8818''45'resp'45''8776'_702 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny -> AgdaAny
v8
                               ~AgdaAny
v9 ~AgdaAny
v10 T_IsHeytingAlgebra_598
v11
  = T_IsHeytingAlgebra_598 -> T_Σ_14
du_'8818''45'resp'45''8776'_702 T_IsHeytingAlgebra_598
v11
du_'8818''45'resp'45''8776'_702 ::
  T_IsHeytingAlgebra_598 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8818''45'resp'45''8776'_702 :: T_IsHeytingAlgebra_598 -> T_Σ_14
du_'8818''45'resp'45''8776'_702 T_IsHeytingAlgebra_598
v0
  = let v1 :: T_IsBoundedLattice_502
v1 = T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> T_IsHeytingAlgebra_598
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_340
v2 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_174
v3 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
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_'8818''45'resp'45''8776'_112
               ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                  (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v3)))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.≲-respʳ-≈
d_'8818''45'resp'691''45''8776'_704 ::
  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_598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'691''45''8776'_704 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_598
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'691''45''8776'_704 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7
                                    ~AgdaAny -> AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10 T_IsHeytingAlgebra_598
v11
  = T_IsHeytingAlgebra_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_704 T_IsHeytingAlgebra_598
v11
du_'8818''45'resp'691''45''8776'_704 ::
  T_IsHeytingAlgebra_598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_704 :: T_IsHeytingAlgebra_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_704 T_IsHeytingAlgebra_598
v0
  = let v1 :: T_IsBoundedLattice_502
v1 = T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> T_IsHeytingAlgebra_598
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_340
v2 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_174
v3 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
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_'8818''45'resp'691''45''8776'_106
               ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                  (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v3)))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.≲-respˡ-≈
d_'8818''45'resp'737''45''8776'_706 ::
  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_598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'737''45''8776'_706 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_598
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'737''45''8776'_706 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7
                                    ~AgdaAny -> AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10 T_IsHeytingAlgebra_598
v11
  = T_IsHeytingAlgebra_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_706 T_IsHeytingAlgebra_598
v11
du_'8818''45'resp'737''45''8776'_706 ::
  T_IsHeytingAlgebra_598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_706 :: T_IsHeytingAlgebra_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_706 T_IsHeytingAlgebra_598
v0
  = let v1 :: T_IsBoundedLattice_502
v1 = T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> T_IsHeytingAlgebra_598
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_340
v2 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_174
v3 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
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_'8818''45'resp'737''45''8776'_100
               ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                  (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v3)))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.Eq.isPartialEquivalence
d_isPartialEquivalence_710 ::
  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_598 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_710 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_598
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_710 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny -> AgdaAny
v8 ~AgdaAny
v9
                           ~AgdaAny
v10 T_IsHeytingAlgebra_598
v11
  = T_IsHeytingAlgebra_598 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_710 T_IsHeytingAlgebra_598
v11
du_isPartialEquivalence_710 ::
  T_IsHeytingAlgebra_598 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_710 :: T_IsHeytingAlgebra_598 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_710 T_IsHeytingAlgebra_598
v0
  = let v1 :: T_IsBoundedLattice_502
v1 = T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> T_IsHeytingAlgebra_598
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_340
v2 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_174
v3 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreorder_70
v4
                   = T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                       (T_IsPartialOrder_174 -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsPartialOrder_174
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.Structures.IsHeytingAlgebra._.Eq.refl
d_refl_712 :: T_IsHeytingAlgebra_598 -> AgdaAny -> AgdaAny
d_refl_712 :: T_IsHeytingAlgebra_598 -> AgdaAny -> AgdaAny
d_refl_712 T_IsHeytingAlgebra_598
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352
               ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 ((T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v0))))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.Eq.reflexive
d_reflexive_714 ::
  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_598 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_714 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_598
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_714 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10 T_IsHeytingAlgebra_598
v11
  = T_IsHeytingAlgebra_598
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_714 T_IsHeytingAlgebra_598
v11
du_reflexive_714 ::
  T_IsHeytingAlgebra_598 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_714 :: T_IsHeytingAlgebra_598
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_714 T_IsHeytingAlgebra_598
v0
  = let v1 :: T_IsBoundedLattice_502
v1 = T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> T_IsHeytingAlgebra_598
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_340
v2 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_174
v3 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreorder_70
v4
                   = T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                       (T_IsPartialOrder_174 -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsPartialOrder_174
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.Structures.IsHeytingAlgebra._.Eq.sym
d_sym_716 ::
  T_IsHeytingAlgebra_598 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_716 :: T_IsHeytingAlgebra_598 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_716 T_IsHeytingAlgebra_598
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352
               ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 ((T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v0))))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.Eq.trans
d_trans_718 ::
  T_IsHeytingAlgebra_598 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_718 :: T_IsHeytingAlgebra_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_718 T_IsHeytingAlgebra_598
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352
               ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 ((T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v0))))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra
d_IsBooleanAlgebra_730 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsBooleanAlgebra_730 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_730
  = C_IsBooleanAlgebra'46'constructor_31651 T_IsHeytingAlgebra_598
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._⇨_
d__'8680'__750 ::
  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_730 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8680'__750 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_730
-> AgdaAny
-> AgdaAny
-> AgdaAny
d__'8680'__750 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10 ~T_IsBooleanAlgebra_730
v11 AgdaAny
v12
               AgdaAny
v13
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'8680'__750 AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny -> AgdaAny
v8 AgdaAny
v12 AgdaAny
v13
du__'8680'__750 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'8680'__750 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'8680'__750 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.Structures.IsBooleanAlgebra.isHeytingAlgebra
d_isHeytingAlgebra_756 ::
  T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598
d_isHeytingAlgebra_756 :: T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598
d_isHeytingAlgebra_756 T_IsBooleanAlgebra_730
v0
  = case T_IsBooleanAlgebra_730 -> T_IsBooleanAlgebra_730
forall a b. a -> b
coe T_IsBooleanAlgebra_730
v0 of
      C_IsBooleanAlgebra'46'constructor_31651 T_IsHeytingAlgebra_598
v1 -> T_IsHeytingAlgebra_598 -> T_IsHeytingAlgebra_598
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v1
      T_IsBooleanAlgebra_730
_ -> T_IsHeytingAlgebra_598
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.antisym
d_antisym_760 ::
  T_IsBooleanAlgebra_730 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_760 :: T_IsBooleanAlgebra_730
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_760 T_IsBooleanAlgebra_730
v0
  = (T_IsPartialOrder_174
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_174
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_184
      ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352
         ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518
            ((T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 ((T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598
d_isHeytingAlgebra_756 (T_IsBooleanAlgebra_730 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_730
v0)))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.exponential
d_exponential_762 ::
  T_IsBooleanAlgebra_730 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_exponential_762 :: T_IsBooleanAlgebra_730 -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
d_exponential_762 T_IsBooleanAlgebra_730
v0
  = (T_IsHeytingAlgebra_598 -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsHeytingAlgebra_598 -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
d_exponential_616 ((T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598
d_isHeytingAlgebra_756 (T_IsBooleanAlgebra_730 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_730
v0))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.infimum
d_infimum_764 ::
  T_IsBooleanAlgebra_730 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_infimum_764 :: T_IsBooleanAlgebra_730 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_764 T_IsBooleanAlgebra_730
v0
  = (T_IsLattice_340 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsLattice_340 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_356
      ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518
         ((T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 ((T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598
d_isHeytingAlgebra_756 (T_IsBooleanAlgebra_730 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_730
v0))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.isBoundedJoinSemilattice
d_isBoundedJoinSemilattice_766 ::
  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_730 -> T_IsBoundedJoinSemilattice_116
d_isBoundedJoinSemilattice_766 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_730
-> T_IsBoundedJoinSemilattice_116
d_isBoundedJoinSemilattice_766 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny
v8
                               ~AgdaAny
v9 ~AgdaAny
v10 T_IsBooleanAlgebra_730
v11
  = T_IsBooleanAlgebra_730 -> T_IsBoundedJoinSemilattice_116
du_isBoundedJoinSemilattice_766 T_IsBooleanAlgebra_730
v11
du_isBoundedJoinSemilattice_766 ::
  T_IsBooleanAlgebra_730 -> T_IsBoundedJoinSemilattice_116
du_isBoundedJoinSemilattice_766 :: T_IsBooleanAlgebra_730 -> T_IsBoundedJoinSemilattice_116
du_isBoundedJoinSemilattice_766 T_IsBooleanAlgebra_730
v0
  = let v1 :: T_IsHeytingAlgebra_598
v1 = T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598
d_isHeytingAlgebra_756 (T_IsBooleanAlgebra_730 -> T_IsBooleanAlgebra_730
forall a b. a -> b
coe T_IsBooleanAlgebra_730
v0) in
    AgdaAny -> T_IsBoundedJoinSemilattice_116
forall a b. a -> b
coe
      ((T_IsBoundedLattice_502 -> T_IsBoundedJoinSemilattice_116)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBoundedLattice_502 -> T_IsBoundedJoinSemilattice_116
du_isBoundedJoinSemilattice_584
         ((T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v1)))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.isBoundedLattice
d_isBoundedLattice_768 ::
  T_IsBooleanAlgebra_730 -> T_IsBoundedLattice_502
d_isBoundedLattice_768 :: T_IsBooleanAlgebra_730 -> T_IsBoundedLattice_502
d_isBoundedLattice_768 T_IsBooleanAlgebra_730
v0
  = (T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502)
-> AgdaAny -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 ((T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598
d_isHeytingAlgebra_756 (T_IsBooleanAlgebra_730 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_730
v0))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.isBoundedMeetSemilattice
d_isBoundedMeetSemilattice_770 ::
  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_730 -> T_IsBoundedMeetSemilattice_274
d_isBoundedMeetSemilattice_770 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_730
-> T_IsBoundedMeetSemilattice_274
d_isBoundedMeetSemilattice_770 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny
v8
                               ~AgdaAny
v9 ~AgdaAny
v10 T_IsBooleanAlgebra_730
v11
  = T_IsBooleanAlgebra_730 -> T_IsBoundedMeetSemilattice_274
du_isBoundedMeetSemilattice_770 T_IsBooleanAlgebra_730
v11
du_isBoundedMeetSemilattice_770 ::
  T_IsBooleanAlgebra_730 -> T_IsBoundedMeetSemilattice_274
du_isBoundedMeetSemilattice_770 :: T_IsBooleanAlgebra_730 -> T_IsBoundedMeetSemilattice_274
du_isBoundedMeetSemilattice_770 T_IsBooleanAlgebra_730
v0
  = let v1 :: T_IsHeytingAlgebra_598
v1 = T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598
d_isHeytingAlgebra_756 (T_IsBooleanAlgebra_730 -> T_IsBooleanAlgebra_730
forall a b. a -> b
coe T_IsBooleanAlgebra_730
v0) in
    AgdaAny -> T_IsBoundedMeetSemilattice_274
forall a b. a -> b
coe
      ((T_IsBoundedLattice_502 -> T_IsBoundedMeetSemilattice_274)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBoundedLattice_502 -> T_IsBoundedMeetSemilattice_274
du_isBoundedMeetSemilattice_586
         ((T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v1)))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.isEquivalence
d_isEquivalence_772 ::
  T_IsBooleanAlgebra_730 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_26
d_isEquivalence_772 :: T_IsBooleanAlgebra_730 -> T_IsEquivalence_26
d_isEquivalence_772 T_IsBooleanAlgebra_730
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352
            ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518
               ((T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 ((T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598
d_isHeytingAlgebra_756 (T_IsBooleanAlgebra_730 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_730
v0))))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.isJoinSemilattice
d_isJoinSemilattice_774 ::
  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_730 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_774 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_730
-> T_IsJoinSemilattice_22
d_isJoinSemilattice_774 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny
v9
                        ~AgdaAny
v10 T_IsBooleanAlgebra_730
v11
  = T_IsBooleanAlgebra_730 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_774 T_IsBooleanAlgebra_730
v11
du_isJoinSemilattice_774 ::
  T_IsBooleanAlgebra_730 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_774 :: T_IsBooleanAlgebra_730 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_774 T_IsBooleanAlgebra_730
v0
  = let v1 :: T_IsHeytingAlgebra_598
v1 = T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598
d_isHeytingAlgebra_756 (T_IsBooleanAlgebra_730 -> T_IsBooleanAlgebra_730
forall a b. a -> b
coe T_IsBooleanAlgebra_730
v0) in
    AgdaAny -> T_IsJoinSemilattice_22
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_502
v2 = T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> T_IsHeytingAlgebra_598
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsLattice_340 -> T_IsJoinSemilattice_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_358 ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502
v2))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.isLattice
d_isLattice_776 :: T_IsBooleanAlgebra_730 -> T_IsLattice_340
d_isLattice_776 :: T_IsBooleanAlgebra_730 -> T_IsLattice_340
d_isLattice_776 T_IsBooleanAlgebra_730
v0
  = (T_IsBoundedLattice_502 -> T_IsLattice_340)
-> AgdaAny -> T_IsLattice_340
forall a b. a -> b
coe
      T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518
      ((T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 ((T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598
d_isHeytingAlgebra_756 (T_IsBooleanAlgebra_730 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_730
v0)))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.isMeetSemilattice
d_isMeetSemilattice_778 ::
  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_730 -> T_IsMeetSemilattice_180
d_isMeetSemilattice_778 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_730
-> T_IsMeetSemilattice_180
d_isMeetSemilattice_778 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny
v9
                        ~AgdaAny
v10 T_IsBooleanAlgebra_730
v11
  = T_IsBooleanAlgebra_730 -> T_IsMeetSemilattice_180
du_isMeetSemilattice_778 T_IsBooleanAlgebra_730
v11
du_isMeetSemilattice_778 ::
  T_IsBooleanAlgebra_730 -> T_IsMeetSemilattice_180
du_isMeetSemilattice_778 :: T_IsBooleanAlgebra_730 -> T_IsMeetSemilattice_180
du_isMeetSemilattice_778 T_IsBooleanAlgebra_730
v0
  = let v1 :: T_IsHeytingAlgebra_598
v1 = T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598
d_isHeytingAlgebra_756 (T_IsBooleanAlgebra_730 -> T_IsBooleanAlgebra_730
forall a b. a -> b
coe T_IsBooleanAlgebra_730
v0) in
    AgdaAny -> T_IsMeetSemilattice_180
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_502
v2 = T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> T_IsHeytingAlgebra_598
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsLattice_340 -> T_IsMeetSemilattice_180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsMeetSemilattice_180
du_isMeetSemilattice_360 ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_502
v2))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.isPartialOrder
d_isPartialOrder_780 ::
  T_IsBooleanAlgebra_730 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_174
d_isPartialOrder_780 :: T_IsBooleanAlgebra_730 -> T_IsPartialOrder_174
d_isPartialOrder_780 T_IsBooleanAlgebra_730
v0
  = (T_IsLattice_340 -> T_IsPartialOrder_174)
-> AgdaAny -> T_IsPartialOrder_174
forall a b. a -> b
coe
      T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352
      ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518
         ((T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 ((T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598
d_isHeytingAlgebra_756 (T_IsBooleanAlgebra_730 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_730
v0))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.isPreorder
d_isPreorder_782 ::
  T_IsBooleanAlgebra_730 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_70
d_isPreorder_782 :: T_IsBooleanAlgebra_730 -> T_IsPreorder_70
d_isPreorder_782 T_IsBooleanAlgebra_730
v0
  = (T_IsPartialOrder_174 -> T_IsPreorder_70)
-> AgdaAny -> T_IsPreorder_70
forall a b. a -> b
coe
      T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
      ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352
         ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518
            ((T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 ((T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598
d_isHeytingAlgebra_756 (T_IsBooleanAlgebra_730 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_730
v0)))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.maximum
d_maximum_784 :: T_IsBooleanAlgebra_730 -> AgdaAny -> AgdaAny
d_maximum_784 :: T_IsBooleanAlgebra_730 -> AgdaAny -> AgdaAny
d_maximum_784 T_IsBooleanAlgebra_730
v0
  = (T_IsBoundedLattice_502 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsBoundedLattice_502 -> AgdaAny -> AgdaAny
d_maximum_520
      ((T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 ((T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598
d_isHeytingAlgebra_756 (T_IsBooleanAlgebra_730 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_730
v0)))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.minimum
d_minimum_786 :: T_IsBooleanAlgebra_730 -> AgdaAny -> AgdaAny
d_minimum_786 :: T_IsBooleanAlgebra_730 -> AgdaAny -> AgdaAny
d_minimum_786 T_IsBooleanAlgebra_730
v0
  = (T_IsBoundedLattice_502 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsBoundedLattice_502 -> AgdaAny -> AgdaAny
d_minimum_522
      ((T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 ((T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598
d_isHeytingAlgebra_756 (T_IsBooleanAlgebra_730 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_730
v0)))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.refl
d_refl_788 ::
  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_730 -> AgdaAny -> AgdaAny
d_refl_788 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_730
-> AgdaAny
-> AgdaAny
d_refl_788 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10 T_IsBooleanAlgebra_730
v11
  = T_IsBooleanAlgebra_730 -> AgdaAny -> AgdaAny
du_refl_788 T_IsBooleanAlgebra_730
v11
du_refl_788 :: T_IsBooleanAlgebra_730 -> AgdaAny -> AgdaAny
du_refl_788 :: T_IsBooleanAlgebra_730 -> AgdaAny -> AgdaAny
du_refl_788 T_IsBooleanAlgebra_730
v0
  = let v1 :: T_IsHeytingAlgebra_598
v1 = T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598
d_isHeytingAlgebra_756 (T_IsBooleanAlgebra_730 -> T_IsBooleanAlgebra_730
forall a b. a -> b
coe T_IsBooleanAlgebra_730
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_502
v2 = T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> T_IsHeytingAlgebra_598
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_340
v3 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_174
v4 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                     (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v4))))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.reflexive
d_reflexive_790 ::
  T_IsBooleanAlgebra_730 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_790 :: T_IsBooleanAlgebra_730 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_790 T_IsBooleanAlgebra_730
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352
            ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518
               ((T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 ((T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598
d_isHeytingAlgebra_756 (T_IsBooleanAlgebra_730 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_730
v0))))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.supremum
d_supremum_792 ::
  T_IsBooleanAlgebra_730 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_supremum_792 :: T_IsBooleanAlgebra_730 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_792 T_IsBooleanAlgebra_730
v0
  = (T_IsLattice_340 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsLattice_340 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_354
      ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518
         ((T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 ((T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598
d_isHeytingAlgebra_756 (T_IsBooleanAlgebra_730 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_730
v0))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.trans
d_trans_794 ::
  T_IsBooleanAlgebra_730 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_794 :: T_IsBooleanAlgebra_730
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_794 T_IsBooleanAlgebra_730
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
         ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352
            ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518
               ((T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 ((T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598
d_isHeytingAlgebra_756 (T_IsBooleanAlgebra_730 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_730
v0))))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.transpose-⇨
d_transpose'45''8680'_796 ::
  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_730 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_transpose'45''8680'_796 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_730
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_transpose'45''8680'_796 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny
v9
                          ~AgdaAny
v10 T_IsBooleanAlgebra_730
v11
  = T_IsBooleanAlgebra_730
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8680'_796 T_IsBooleanAlgebra_730
v11
du_transpose'45''8680'_796 ::
  T_IsBooleanAlgebra_730 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8680'_796 :: T_IsBooleanAlgebra_730
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8680'_796 T_IsBooleanAlgebra_730
v0
  = (T_IsHeytingAlgebra_598
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsHeytingAlgebra_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8680'_624 ((T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598
d_isHeytingAlgebra_756 (T_IsBooleanAlgebra_730 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_730
v0))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.transpose-∧
d_transpose'45''8743'_798 ::
  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_730 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_transpose'45''8743'_798 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_730
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_transpose'45''8743'_798 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny
v9
                          ~AgdaAny
v10 T_IsBooleanAlgebra_730
v11
  = T_IsBooleanAlgebra_730
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8743'_798 T_IsBooleanAlgebra_730
v11
du_transpose'45''8743'_798 ::
  T_IsBooleanAlgebra_730 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8743'_798 :: T_IsBooleanAlgebra_730
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8743'_798 T_IsBooleanAlgebra_730
v0
  = (T_IsHeytingAlgebra_598
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsHeytingAlgebra_598
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8743'_640 ((T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598
d_isHeytingAlgebra_756 (T_IsBooleanAlgebra_730 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_730
v0))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.x∧y≤x
d_x'8743'y'8804'x_800 ::
  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_730 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'x_800 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_730
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'x_800 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10
                      T_IsBooleanAlgebra_730
v11
  = T_IsBooleanAlgebra_730 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_800 T_IsBooleanAlgebra_730
v11
du_x'8743'y'8804'x_800 ::
  T_IsBooleanAlgebra_730 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_800 :: T_IsBooleanAlgebra_730 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_800 T_IsBooleanAlgebra_730
v0
  = let v1 :: T_IsHeytingAlgebra_598
v1 = T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598
d_isHeytingAlgebra_756 (T_IsBooleanAlgebra_730 -> T_IsBooleanAlgebra_730
forall a b. a -> b
coe T_IsBooleanAlgebra_730
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_502
v2 = T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> T_IsHeytingAlgebra_598
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_340
v3 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_196 ((T_IsLattice_340 -> T_IsMeetSemilattice_180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsMeetSemilattice_180
du_isMeetSemilattice_360 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v3)))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.x∧y≤y
d_x'8743'y'8804'y_802 ::
  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_730 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'y_802 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_730
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'y_802 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10
                      T_IsBooleanAlgebra_730
v11
  = T_IsBooleanAlgebra_730 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_802 T_IsBooleanAlgebra_730
v11
du_x'8743'y'8804'y_802 ::
  T_IsBooleanAlgebra_730 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_802 :: T_IsBooleanAlgebra_730 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_802 T_IsBooleanAlgebra_730
v0
  = let v1 :: T_IsHeytingAlgebra_598
v1 = T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598
d_isHeytingAlgebra_756 (T_IsBooleanAlgebra_730 -> T_IsBooleanAlgebra_730
forall a b. a -> b
coe T_IsBooleanAlgebra_730
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_502
v2 = T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> T_IsHeytingAlgebra_598
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_340
v3 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMeetSemilattice_180 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_208 ((T_IsLattice_340 -> T_IsMeetSemilattice_180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsMeetSemilattice_180
du_isMeetSemilattice_360 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v3)))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.x≤x∨y
d_x'8804'x'8744'y_804 ::
  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_730 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8804'x'8744'y_804 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_730
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8804'x'8744'y_804 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10
                      T_IsBooleanAlgebra_730
v11
  = T_IsBooleanAlgebra_730 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_804 T_IsBooleanAlgebra_730
v11
du_x'8804'x'8744'y_804 ::
  T_IsBooleanAlgebra_730 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_804 :: T_IsBooleanAlgebra_730 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_804 T_IsBooleanAlgebra_730
v0
  = let v1 :: T_IsHeytingAlgebra_598
v1 = T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598
d_isHeytingAlgebra_756 (T_IsBooleanAlgebra_730 -> T_IsBooleanAlgebra_730
forall a b. a -> b
coe T_IsBooleanAlgebra_730
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_502
v2 = T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> T_IsHeytingAlgebra_598
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_340
v3 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_38 ((T_IsLattice_340 -> T_IsJoinSemilattice_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_358 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v3)))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.y≤x∨y
d_y'8804'x'8744'y_806 ::
  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_730 -> AgdaAny -> AgdaAny -> AgdaAny
d_y'8804'x'8744'y_806 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_730
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_y'8804'x'8744'y_806 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10
                      T_IsBooleanAlgebra_730
v11
  = T_IsBooleanAlgebra_730 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_806 T_IsBooleanAlgebra_730
v11
du_y'8804'x'8744'y_806 ::
  T_IsBooleanAlgebra_730 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_806 :: T_IsBooleanAlgebra_730 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_806 T_IsBooleanAlgebra_730
v0
  = let v1 :: T_IsHeytingAlgebra_598
v1 = T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598
d_isHeytingAlgebra_756 (T_IsBooleanAlgebra_730 -> T_IsBooleanAlgebra_730
forall a b. a -> b
coe T_IsBooleanAlgebra_730
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_502
v2 = T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> T_IsHeytingAlgebra_598
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_340
v3 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsJoinSemilattice_22 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_50 ((T_IsLattice_340 -> T_IsJoinSemilattice_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_358 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v3)))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.∧-greatest
d_'8743''45'greatest_808 ::
  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_730 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'greatest_808 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_730
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'greatest_808 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny
v9
                         ~AgdaAny
v10 T_IsBooleanAlgebra_730
v11
  = T_IsBooleanAlgebra_730
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_808 T_IsBooleanAlgebra_730
v11
du_'8743''45'greatest_808 ::
  T_IsBooleanAlgebra_730 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_808 :: T_IsBooleanAlgebra_730
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_808 T_IsBooleanAlgebra_730
v0
  = let v1 :: T_IsHeytingAlgebra_598
v1 = T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598
d_isHeytingAlgebra_756 (T_IsBooleanAlgebra_730 -> T_IsBooleanAlgebra_730
forall a b. a -> b
coe T_IsBooleanAlgebra_730
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_502
v2 = T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> T_IsHeytingAlgebra_598
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_340
v3 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMeetSemilattice_180
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMeetSemilattice_180
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_222
               ((T_IsLattice_340 -> T_IsMeetSemilattice_180) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsMeetSemilattice_180
du_isMeetSemilattice_360 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v3)))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.∨-least
d_'8744''45'least_810 ::
  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_730 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'least_810 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_730
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'least_810 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10
                      T_IsBooleanAlgebra_730
v11
  = T_IsBooleanAlgebra_730
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_810 T_IsBooleanAlgebra_730
v11
du_'8744''45'least_810 ::
  T_IsBooleanAlgebra_730 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_810 :: T_IsBooleanAlgebra_730
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_810 T_IsBooleanAlgebra_730
v0
  = let v1 :: T_IsHeytingAlgebra_598
v1 = T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598
d_isHeytingAlgebra_756 (T_IsBooleanAlgebra_730 -> T_IsBooleanAlgebra_730
forall a b. a -> b
coe T_IsBooleanAlgebra_730
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_502
v2 = T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> T_IsHeytingAlgebra_598
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_340
v3 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsJoinSemilattice_22
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsJoinSemilattice_22
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_64 ((T_IsLattice_340 -> T_IsJoinSemilattice_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_358 (T_IsLattice_340 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_340
v3)))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.∼-resp-≈
d_'8764''45'resp'45''8776'_812 ::
  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_730 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_812 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_730
-> T_Σ_14
d_'8764''45'resp'45''8776'_812 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny
v8
                               ~AgdaAny
v9 ~AgdaAny
v10 T_IsBooleanAlgebra_730
v11
  = T_IsBooleanAlgebra_730 -> T_Σ_14
du_'8764''45'resp'45''8776'_812 T_IsBooleanAlgebra_730
v11
du_'8764''45'resp'45''8776'_812 ::
  T_IsBooleanAlgebra_730 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_812 :: T_IsBooleanAlgebra_730 -> T_Σ_14
du_'8764''45'resp'45''8776'_812 T_IsBooleanAlgebra_730
v0
  = let v1 :: T_IsHeytingAlgebra_598
v1 = T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598
d_isHeytingAlgebra_756 (T_IsBooleanAlgebra_730 -> T_IsBooleanAlgebra_730
forall a b. a -> b
coe T_IsBooleanAlgebra_730
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_502
v2 = T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> T_IsHeytingAlgebra_598
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_340
v3 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_174
v4 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
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'_118
                  ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                     (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v4))))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_814 ::
  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_730 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_814 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_730
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_814 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7
                                    ~AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10 T_IsBooleanAlgebra_730
v11
  = T_IsBooleanAlgebra_730
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_814 T_IsBooleanAlgebra_730
v11
du_'8764''45'resp'691''45''8776'_814 ::
  T_IsBooleanAlgebra_730 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_814 :: T_IsBooleanAlgebra_730
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_814 T_IsBooleanAlgebra_730
v0
  = let v1 :: T_IsHeytingAlgebra_598
v1 = T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598
d_isHeytingAlgebra_756 (T_IsBooleanAlgebra_730 -> T_IsBooleanAlgebra_730
forall a b. a -> b
coe T_IsBooleanAlgebra_730
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_502
v2 = T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> T_IsHeytingAlgebra_598
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_340
v3 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_174
v4 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
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'_116
                  ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                     (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v4))))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_816 ::
  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_730 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_816 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_730
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_816 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7
                                    ~AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10 T_IsBooleanAlgebra_730
v11
  = T_IsBooleanAlgebra_730
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_816 T_IsBooleanAlgebra_730
v11
du_'8764''45'resp'737''45''8776'_816 ::
  T_IsBooleanAlgebra_730 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_816 :: T_IsBooleanAlgebra_730
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_816 T_IsBooleanAlgebra_730
v0
  = let v1 :: T_IsHeytingAlgebra_598
v1 = T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598
d_isHeytingAlgebra_756 (T_IsBooleanAlgebra_730 -> T_IsBooleanAlgebra_730
forall a b. a -> b
coe T_IsBooleanAlgebra_730
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_502
v2 = T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> T_IsHeytingAlgebra_598
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_340
v3 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_174
v4 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
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'_114
                  ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                     (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v4))))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.≲-resp-≈
d_'8818''45'resp'45''8776'_818 ::
  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_730 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8818''45'resp'45''8776'_818 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_730
-> T_Σ_14
d_'8818''45'resp'45''8776'_818 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny
v8
                               ~AgdaAny
v9 ~AgdaAny
v10 T_IsBooleanAlgebra_730
v11
  = T_IsBooleanAlgebra_730 -> T_Σ_14
du_'8818''45'resp'45''8776'_818 T_IsBooleanAlgebra_730
v11
du_'8818''45'resp'45''8776'_818 ::
  T_IsBooleanAlgebra_730 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8818''45'resp'45''8776'_818 :: T_IsBooleanAlgebra_730 -> T_Σ_14
du_'8818''45'resp'45''8776'_818 T_IsBooleanAlgebra_730
v0
  = let v1 :: T_IsHeytingAlgebra_598
v1 = T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598
d_isHeytingAlgebra_756 (T_IsBooleanAlgebra_730 -> T_IsBooleanAlgebra_730
forall a b. a -> b
coe T_IsBooleanAlgebra_730
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_502
v2 = T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> T_IsHeytingAlgebra_598
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_340
v3 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_174
v4 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
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_'8818''45'resp'45''8776'_112
                  ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                     (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v4))))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.≲-respʳ-≈
d_'8818''45'resp'691''45''8776'_820 ::
  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_730 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'691''45''8776'_820 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_730
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'691''45''8776'_820 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7
                                    ~AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10 T_IsBooleanAlgebra_730
v11
  = T_IsBooleanAlgebra_730
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_820 T_IsBooleanAlgebra_730
v11
du_'8818''45'resp'691''45''8776'_820 ::
  T_IsBooleanAlgebra_730 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_820 :: T_IsBooleanAlgebra_730
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_820 T_IsBooleanAlgebra_730
v0
  = let v1 :: T_IsHeytingAlgebra_598
v1 = T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598
d_isHeytingAlgebra_756 (T_IsBooleanAlgebra_730 -> T_IsBooleanAlgebra_730
forall a b. a -> b
coe T_IsBooleanAlgebra_730
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_502
v2 = T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> T_IsHeytingAlgebra_598
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_340
v3 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_174
v4 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
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_'8818''45'resp'691''45''8776'_106
                  ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                     (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v4))))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.≲-respˡ-≈
d_'8818''45'resp'737''45''8776'_822 ::
  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_730 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'737''45''8776'_822 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_730
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'737''45''8776'_822 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7
                                    ~AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10 T_IsBooleanAlgebra_730
v11
  = T_IsBooleanAlgebra_730
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_822 T_IsBooleanAlgebra_730
v11
du_'8818''45'resp'737''45''8776'_822 ::
  T_IsBooleanAlgebra_730 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_822 :: T_IsBooleanAlgebra_730
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_822 T_IsBooleanAlgebra_730
v0
  = let v1 :: T_IsHeytingAlgebra_598
v1 = T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598
d_isHeytingAlgebra_756 (T_IsBooleanAlgebra_730 -> T_IsBooleanAlgebra_730
forall a b. a -> b
coe T_IsBooleanAlgebra_730
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_502
v2 = T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> T_IsHeytingAlgebra_598
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_340
v3 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_174
v4 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
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_'8818''45'resp'737''45''8776'_100
                  ((T_IsPartialOrder_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                     (T_IsPartialOrder_174 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_174
v4))))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.Eq.isPartialEquivalence
d_isPartialEquivalence_826 ::
  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_730 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_826 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_730
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_826 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny
v9
                           ~AgdaAny
v10 T_IsBooleanAlgebra_730
v11
  = T_IsBooleanAlgebra_730 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_826 T_IsBooleanAlgebra_730
v11
du_isPartialEquivalence_826 ::
  T_IsBooleanAlgebra_730 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_826 :: T_IsBooleanAlgebra_730 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_826 T_IsBooleanAlgebra_730
v0
  = let v1 :: T_IsHeytingAlgebra_598
v1 = T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598
d_isHeytingAlgebra_756 (T_IsBooleanAlgebra_730 -> T_IsBooleanAlgebra_730
forall a b. a -> b
coe T_IsBooleanAlgebra_730
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_502
v2 = T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> T_IsHeytingAlgebra_598
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_340
v3 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_174
v4 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPreorder_70
v5
                      = T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                          (T_IsPartialOrder_174 -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsPartialOrder_174
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.Structures.IsBooleanAlgebra._.Eq.refl
d_refl_828 :: T_IsBooleanAlgebra_730 -> AgdaAny -> AgdaAny
d_refl_828 :: T_IsBooleanAlgebra_730 -> AgdaAny -> AgdaAny
d_refl_828 T_IsBooleanAlgebra_730
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352
               ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518
                  ((T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 ((T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598
d_isHeytingAlgebra_756 (T_IsBooleanAlgebra_730 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_730
v0)))))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.Eq.reflexive
d_reflexive_830 ::
  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_730 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_830 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_730
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_830 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny -> AgdaAny
v8 ~AgdaAny
v9 ~AgdaAny
v10 T_IsBooleanAlgebra_730
v11
  = T_IsBooleanAlgebra_730
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_830 T_IsBooleanAlgebra_730
v11
du_reflexive_830 ::
  T_IsBooleanAlgebra_730 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_830 :: T_IsBooleanAlgebra_730
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_830 T_IsBooleanAlgebra_730
v0
  = let v1 :: T_IsHeytingAlgebra_598
v1 = T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598
d_isHeytingAlgebra_756 (T_IsBooleanAlgebra_730 -> T_IsBooleanAlgebra_730
forall a b. a -> b
coe T_IsBooleanAlgebra_730
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_502
v2 = T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 (T_IsHeytingAlgebra_598 -> T_IsHeytingAlgebra_598
forall a b. a -> b
coe T_IsHeytingAlgebra_598
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_340
v3 = T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518 (T_IsBoundedLattice_502 -> T_IsBoundedLattice_502
forall a b. a -> b
coe T_IsBoundedLattice_502
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_174
v4 = T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352 (T_IsLattice_340 -> T_IsLattice_340
forall a b. a -> b
coe T_IsLattice_340
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPreorder_70
v5
                      = T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
                          (T_IsPartialOrder_174 -> T_IsPartialOrder_174
forall a b. a -> b
coe T_IsPartialOrder_174
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.Structures.IsBooleanAlgebra._.Eq.sym
d_sym_832 ::
  T_IsBooleanAlgebra_730 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_832 :: T_IsBooleanAlgebra_730 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_832 T_IsBooleanAlgebra_730
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352
               ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518
                  ((T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 ((T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598
d_isHeytingAlgebra_756 (T_IsBooleanAlgebra_730 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_730
v0)))))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.Eq.trans
d_trans_834 ::
  T_IsBooleanAlgebra_730 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_834 :: T_IsBooleanAlgebra_730
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_834 T_IsBooleanAlgebra_730
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_174 -> T_IsPreorder_70) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_174 -> T_IsPreorder_70
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_182
            ((T_IsLattice_340 -> T_IsPartialOrder_174) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_340 -> T_IsPartialOrder_174
d_isPartialOrder_352
               ((T_IsBoundedLattice_502 -> T_IsLattice_340) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBoundedLattice_502 -> T_IsLattice_340
d_isLattice_518
                  ((T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsHeytingAlgebra_598 -> T_IsBoundedLattice_502
d_isBoundedLattice_614 ((T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_730 -> T_IsHeytingAlgebra_598
d_isHeytingAlgebra_756 (T_IsBooleanAlgebra_730 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_730
v0)))))))