{-# 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_constructor_112 MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_248
                      (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_248
d_isPartialOrder_30 :: T_IsJoinSemilattice_22 -> T_IsPartialOrder_248
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_constructor_112 T_IsPartialOrder_248
v1 AgdaAny -> AgdaAny -> T_Σ_14
v2 -> T_IsPartialOrder_248 -> T_IsPartialOrder_248
forall a b. a -> b
coe T_IsPartialOrder_248
v1
      T_IsJoinSemilattice_22
_ -> T_IsPartialOrder_248
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_constructor_112 T_IsPartialOrder_248
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_248
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_248
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_258
      ((T_IsJoinSemilattice_22 -> T_IsPartialOrder_248)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> T_IsPartialOrder_248
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_28
d_isEquivalence_78 :: T_IsJoinSemilattice_22 -> T_IsEquivalence_28
d_isEquivalence_78 T_IsJoinSemilattice_22
v0
  = (T_IsPreorder_76 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsJoinSemilattice_22 -> T_IsPartialOrder_248)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> T_IsPartialOrder_248
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_76
d_isPreorder_80 :: T_IsJoinSemilattice_22 -> T_IsPreorder_76
d_isPreorder_80 T_IsJoinSemilattice_22
v0
  = (T_IsPartialOrder_248 -> T_IsPreorder_76)
-> AgdaAny -> T_IsPreorder_76
forall a b. a -> b
coe
      T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
      ((T_IsJoinSemilattice_22 -> T_IsPartialOrder_248)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> T_IsPartialOrder_248
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_248
v1 = T_IsJoinSemilattice_22 -> T_IsPartialOrder_248
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_76 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_104
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256 (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
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_76 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_76 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_88
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsJoinSemilattice_22 -> T_IsPartialOrder_248)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> T_IsPartialOrder_248
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_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_90
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsJoinSemilattice_22 -> T_IsPartialOrder_248)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> T_IsPartialOrder_248
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_248
v1 = T_IsJoinSemilattice_22 -> T_IsPartialOrder_248
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_76 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_124
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256 (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
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_248
v1 = T_IsJoinSemilattice_22 -> T_IsPartialOrder_248
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_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_122
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256 (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
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_248
v1 = T_IsJoinSemilattice_22 -> T_IsPartialOrder_248
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_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_120
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256 (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
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_248
v1 = T_IsJoinSemilattice_22 -> T_IsPartialOrder_248
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_76 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'45''8776'_118
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256 (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
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_248
v1 = T_IsJoinSemilattice_22 -> T_IsPartialOrder_248
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_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'691''45''8776'_112
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256 (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
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_248
v1 = T_IsJoinSemilattice_22 -> T_IsPartialOrder_248
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_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'737''45''8776'_106
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256 (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
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_248
v1 = T_IsJoinSemilattice_22 -> T_IsPartialOrder_248
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_76
v2
             = T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                 (T_IsPartialOrder_248 -> T_IsPartialOrder_248
forall a b. a -> b
coe T_IsPartialOrder_248
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
               (T_IsPreorder_76 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_76
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_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsJoinSemilattice_22 -> T_IsPartialOrder_248)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> T_IsPartialOrder_248
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_248
v1 = T_IsJoinSemilattice_22 -> T_IsPartialOrder_248
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_76
v2
             = T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                 (T_IsPartialOrder_248 -> T_IsPartialOrder_248
forall a b. a -> b
coe T_IsPartialOrder_248
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
              ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
                 (T_IsPreorder_76 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_76
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_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsJoinSemilattice_22 -> T_IsPartialOrder_248)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> T_IsPartialOrder_248
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_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsJoinSemilattice_22 -> T_IsPartialOrder_248)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> T_IsPartialOrder_248
d_isPartialOrder_30 (T_IsJoinSemilattice_22 -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22
v0))))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice
d_IsBoundedJoinSemilattice_118 :: p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsBoundedJoinSemilattice_118 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 = ()
data T_IsBoundedJoinSemilattice_118
  = C_constructor_180 T_IsJoinSemilattice_22 (AgdaAny -> AgdaAny)
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice.isJoinSemilattice
d_isJoinSemilattice_128 ::
  T_IsBoundedJoinSemilattice_118 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_128 :: T_IsBoundedJoinSemilattice_118 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_128 T_IsBoundedJoinSemilattice_118
v0
  = case T_IsBoundedJoinSemilattice_118 -> T_IsBoundedJoinSemilattice_118
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_118
v0 of
      C_constructor_180 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_118
_ -> T_IsJoinSemilattice_22
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice.minimum
d_minimum_130 ::
  T_IsBoundedJoinSemilattice_118 -> AgdaAny -> AgdaAny
d_minimum_130 :: T_IsBoundedJoinSemilattice_118 -> AgdaAny -> AgdaAny
d_minimum_130 T_IsBoundedJoinSemilattice_118
v0
  = case T_IsBoundedJoinSemilattice_118 -> T_IsBoundedJoinSemilattice_118
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_118
v0 of
      C_constructor_180 T_IsJoinSemilattice_22
v1 AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_IsBoundedJoinSemilattice_118
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.antisym
d_antisym_134 ::
  T_IsBoundedJoinSemilattice_118 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_134 :: T_IsBoundedJoinSemilattice_118
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_134 T_IsBoundedJoinSemilattice_118
v0
  = (T_IsPartialOrder_248
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_248
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_258
      ((T_IsJoinSemilattice_22 -> T_IsPartialOrder_248)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> T_IsPartialOrder_248
d_isPartialOrder_30 ((T_IsBoundedJoinSemilattice_118 -> T_IsJoinSemilattice_22)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_118 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_128 (T_IsBoundedJoinSemilattice_118 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_118
v0)))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.isEquivalence
d_isEquivalence_136 ::
  T_IsBoundedJoinSemilattice_118 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_136 :: T_IsBoundedJoinSemilattice_118 -> T_IsEquivalence_28
d_isEquivalence_136 T_IsBoundedJoinSemilattice_118
v0
  = (T_IsPreorder_76 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsJoinSemilattice_22 -> T_IsPartialOrder_248)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> T_IsPartialOrder_248
d_isPartialOrder_30 ((T_IsBoundedJoinSemilattice_118 -> T_IsJoinSemilattice_22)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_118 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_128 (T_IsBoundedJoinSemilattice_118 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_118
v0))))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.isPartialOrder
d_isPartialOrder_138 ::
  T_IsBoundedJoinSemilattice_118 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_248
d_isPartialOrder_138 :: T_IsBoundedJoinSemilattice_118 -> T_IsPartialOrder_248
d_isPartialOrder_138 T_IsBoundedJoinSemilattice_118
v0
  = (T_IsJoinSemilattice_22 -> T_IsPartialOrder_248)
-> AgdaAny -> T_IsPartialOrder_248
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> T_IsPartialOrder_248
d_isPartialOrder_30 ((T_IsBoundedJoinSemilattice_118 -> T_IsJoinSemilattice_22)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_118 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_128 (T_IsBoundedJoinSemilattice_118 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_118
v0))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.isPreorder
d_isPreorder_140 ::
  T_IsBoundedJoinSemilattice_118 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_76
d_isPreorder_140 :: T_IsBoundedJoinSemilattice_118 -> T_IsPreorder_76
d_isPreorder_140 T_IsBoundedJoinSemilattice_118
v0
  = (T_IsPartialOrder_248 -> T_IsPreorder_76)
-> AgdaAny -> T_IsPreorder_76
forall a b. a -> b
coe
      T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
      ((T_IsJoinSemilattice_22 -> T_IsPartialOrder_248)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> T_IsPartialOrder_248
d_isPartialOrder_30 ((T_IsBoundedJoinSemilattice_118 -> T_IsJoinSemilattice_22)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_118 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_128 (T_IsBoundedJoinSemilattice_118 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_118
v0)))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.refl
d_refl_142 ::
  MAlonzo.Code.Agda.Primitive.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_118 -> AgdaAny -> AgdaAny
d_refl_142 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedJoinSemilattice_118
-> AgdaAny
-> AgdaAny
d_refl_142 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedJoinSemilattice_118
v8 = T_IsBoundedJoinSemilattice_118 -> AgdaAny -> AgdaAny
du_refl_142 T_IsBoundedJoinSemilattice_118
v8
du_refl_142 :: T_IsBoundedJoinSemilattice_118 -> AgdaAny -> AgdaAny
du_refl_142 :: T_IsBoundedJoinSemilattice_118 -> AgdaAny -> AgdaAny
du_refl_142 T_IsBoundedJoinSemilattice_118
v0
  = let v1 :: T_IsJoinSemilattice_22
v1 = T_IsBoundedJoinSemilattice_118 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_128 (T_IsBoundedJoinSemilattice_118 -> T_IsBoundedJoinSemilattice_118
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_118
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsJoinSemilattice_22 -> T_IsPartialOrder_248
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_76 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_76 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_104
            ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
               (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.reflexive
d_reflexive_144 ::
  T_IsBoundedJoinSemilattice_118 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_144 :: T_IsBoundedJoinSemilattice_118
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_144 T_IsBoundedJoinSemilattice_118
v0
  = (T_IsPreorder_76 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_76 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_88
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsJoinSemilattice_22 -> T_IsPartialOrder_248)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> T_IsPartialOrder_248
d_isPartialOrder_30 ((T_IsBoundedJoinSemilattice_118 -> T_IsJoinSemilattice_22)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_118 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_128 (T_IsBoundedJoinSemilattice_118 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_118
v0))))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.supremum
d_supremum_146 ::
  T_IsBoundedJoinSemilattice_118 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_supremum_146 :: T_IsBoundedJoinSemilattice_118 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_146 T_IsBoundedJoinSemilattice_118
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_118 -> T_IsJoinSemilattice_22)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_118 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_128 (T_IsBoundedJoinSemilattice_118 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_118
v0))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.trans
d_trans_148 ::
  T_IsBoundedJoinSemilattice_118 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_148 :: T_IsBoundedJoinSemilattice_118
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_148 T_IsBoundedJoinSemilattice_118
v0
  = (T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_90
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsJoinSemilattice_22 -> T_IsPartialOrder_248)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> T_IsPartialOrder_248
d_isPartialOrder_30 ((T_IsBoundedJoinSemilattice_118 -> T_IsJoinSemilattice_22)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_118 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_128 (T_IsBoundedJoinSemilattice_118 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_118
v0))))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.x≤x∨y
d_x'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_118 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8804'x'8744'y_150 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedJoinSemilattice_118
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8804'x'8744'y_150 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedJoinSemilattice_118
v8
  = T_IsBoundedJoinSemilattice_118 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_150 T_IsBoundedJoinSemilattice_118
v8
du_x'8804'x'8744'y_150 ::
  T_IsBoundedJoinSemilattice_118 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_150 :: T_IsBoundedJoinSemilattice_118 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_150 T_IsBoundedJoinSemilattice_118
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_118 -> T_IsJoinSemilattice_22)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_118 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_128 (T_IsBoundedJoinSemilattice_118 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_118
v0))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.y≤x∨y
d_y'8804'x'8744'y_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_118 -> AgdaAny -> AgdaAny -> AgdaAny
d_y'8804'x'8744'y_152 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedJoinSemilattice_118
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_y'8804'x'8744'y_152 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedJoinSemilattice_118
v8
  = T_IsBoundedJoinSemilattice_118 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_152 T_IsBoundedJoinSemilattice_118
v8
du_y'8804'x'8744'y_152 ::
  T_IsBoundedJoinSemilattice_118 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_152 :: T_IsBoundedJoinSemilattice_118 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_152 T_IsBoundedJoinSemilattice_118
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_118 -> T_IsJoinSemilattice_22)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_118 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_128 (T_IsBoundedJoinSemilattice_118 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_118
v0))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.∨-least
d_'8744''45'least_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_118 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'least_154 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedJoinSemilattice_118
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'least_154 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedJoinSemilattice_118
v8
  = T_IsBoundedJoinSemilattice_118
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_154 T_IsBoundedJoinSemilattice_118
v8
du_'8744''45'least_154 ::
  T_IsBoundedJoinSemilattice_118 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_154 :: T_IsBoundedJoinSemilattice_118
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_154 T_IsBoundedJoinSemilattice_118
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_118 -> T_IsJoinSemilattice_22)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_118 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_128 (T_IsBoundedJoinSemilattice_118 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_118
v0))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.∼-resp-≈
d_'8764''45'resp'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_118 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_156 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedJoinSemilattice_118
-> T_Σ_14
d_'8764''45'resp'45''8776'_156 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedJoinSemilattice_118
v8
  = T_IsBoundedJoinSemilattice_118 -> T_Σ_14
du_'8764''45'resp'45''8776'_156 T_IsBoundedJoinSemilattice_118
v8
du_'8764''45'resp'45''8776'_156 ::
  T_IsBoundedJoinSemilattice_118 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_156 :: T_IsBoundedJoinSemilattice_118 -> T_Σ_14
du_'8764''45'resp'45''8776'_156 T_IsBoundedJoinSemilattice_118
v0
  = let v1 :: T_IsJoinSemilattice_22
v1 = T_IsBoundedJoinSemilattice_118 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_128 (T_IsBoundedJoinSemilattice_118 -> T_IsBoundedJoinSemilattice_118
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_118
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsJoinSemilattice_22 -> T_IsPartialOrder_248
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_76 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_76 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_124
            ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
               (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.∼-respʳ-≈
d_'8764''45'resp'691''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_118 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_158 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedJoinSemilattice_118
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_158 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7
                                    T_IsBoundedJoinSemilattice_118
v8
  = T_IsBoundedJoinSemilattice_118
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_158 T_IsBoundedJoinSemilattice_118
v8
du_'8764''45'resp'691''45''8776'_158 ::
  T_IsBoundedJoinSemilattice_118 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_158 :: T_IsBoundedJoinSemilattice_118
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_158 T_IsBoundedJoinSemilattice_118
v0
  = let v1 :: T_IsJoinSemilattice_22
v1 = T_IsBoundedJoinSemilattice_118 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_128 (T_IsBoundedJoinSemilattice_118 -> T_IsBoundedJoinSemilattice_118
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_118
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsJoinSemilattice_22 -> T_IsPartialOrder_248
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_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_122
            ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
               (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.∼-respˡ-≈
d_'8764''45'resp'737''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_118 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_160 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedJoinSemilattice_118
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_160 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7
                                    T_IsBoundedJoinSemilattice_118
v8
  = T_IsBoundedJoinSemilattice_118
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_160 T_IsBoundedJoinSemilattice_118
v8
du_'8764''45'resp'737''45''8776'_160 ::
  T_IsBoundedJoinSemilattice_118 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_160 :: T_IsBoundedJoinSemilattice_118
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_160 T_IsBoundedJoinSemilattice_118
v0
  = let v1 :: T_IsJoinSemilattice_22
v1 = T_IsBoundedJoinSemilattice_118 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_128 (T_IsBoundedJoinSemilattice_118 -> T_IsBoundedJoinSemilattice_118
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_118
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsJoinSemilattice_22 -> T_IsPartialOrder_248
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_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_120
            ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
               (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.≲-resp-≈
d_'8818''45'resp'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_118 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8818''45'resp'45''8776'_162 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedJoinSemilattice_118
-> T_Σ_14
d_'8818''45'resp'45''8776'_162 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedJoinSemilattice_118
v8
  = T_IsBoundedJoinSemilattice_118 -> T_Σ_14
du_'8818''45'resp'45''8776'_162 T_IsBoundedJoinSemilattice_118
v8
du_'8818''45'resp'45''8776'_162 ::
  T_IsBoundedJoinSemilattice_118 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8818''45'resp'45''8776'_162 :: T_IsBoundedJoinSemilattice_118 -> T_Σ_14
du_'8818''45'resp'45''8776'_162 T_IsBoundedJoinSemilattice_118
v0
  = let v1 :: T_IsJoinSemilattice_22
v1 = T_IsBoundedJoinSemilattice_118 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_128 (T_IsBoundedJoinSemilattice_118 -> T_IsBoundedJoinSemilattice_118
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_118
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsJoinSemilattice_22 -> T_IsPartialOrder_248
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_76 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_76 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'45''8776'_118
            ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
               (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.≲-respʳ-≈
d_'8818''45'resp'691''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_118 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'691''45''8776'_164 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedJoinSemilattice_118
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'691''45''8776'_164 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7
                                    T_IsBoundedJoinSemilattice_118
v8
  = T_IsBoundedJoinSemilattice_118
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_164 T_IsBoundedJoinSemilattice_118
v8
du_'8818''45'resp'691''45''8776'_164 ::
  T_IsBoundedJoinSemilattice_118 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_164 :: T_IsBoundedJoinSemilattice_118
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_164 T_IsBoundedJoinSemilattice_118
v0
  = let v1 :: T_IsJoinSemilattice_22
v1 = T_IsBoundedJoinSemilattice_118 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_128 (T_IsBoundedJoinSemilattice_118 -> T_IsBoundedJoinSemilattice_118
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_118
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsJoinSemilattice_22 -> T_IsPartialOrder_248
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_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'691''45''8776'_112
            ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
               (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.≲-respˡ-≈
d_'8818''45'resp'737''45''8776'_166 ::
  MAlonzo.Code.Agda.Primitive.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_118 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'737''45''8776'_166 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedJoinSemilattice_118
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'737''45''8776'_166 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7
                                    T_IsBoundedJoinSemilattice_118
v8
  = T_IsBoundedJoinSemilattice_118
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_166 T_IsBoundedJoinSemilattice_118
v8
du_'8818''45'resp'737''45''8776'_166 ::
  T_IsBoundedJoinSemilattice_118 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_166 :: T_IsBoundedJoinSemilattice_118
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_166 T_IsBoundedJoinSemilattice_118
v0
  = let v1 :: T_IsJoinSemilattice_22
v1 = T_IsBoundedJoinSemilattice_118 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_128 (T_IsBoundedJoinSemilattice_118 -> T_IsBoundedJoinSemilattice_118
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_118
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsJoinSemilattice_22 -> T_IsPartialOrder_248
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_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'737''45''8776'_106
            ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
               (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.Eq.isPartialEquivalence
d_isPartialEquivalence_170 ::
  MAlonzo.Code.Agda.Primitive.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_118 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_170 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedJoinSemilattice_118
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_170 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedJoinSemilattice_118
v8
  = T_IsBoundedJoinSemilattice_118 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_170 T_IsBoundedJoinSemilattice_118
v8
du_isPartialEquivalence_170 ::
  T_IsBoundedJoinSemilattice_118 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_170 :: T_IsBoundedJoinSemilattice_118 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_170 T_IsBoundedJoinSemilattice_118
v0
  = let v1 :: T_IsJoinSemilattice_22
v1 = T_IsBoundedJoinSemilattice_118 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_128 (T_IsBoundedJoinSemilattice_118 -> T_IsBoundedJoinSemilattice_118
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_118
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsJoinSemilattice_22 -> T_IsPartialOrder_248
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_76
v3
                = T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                    (T_IsPartialOrder_248 -> T_IsPartialOrder_248
forall a b. a -> b
coe T_IsPartialOrder_248
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
                  (T_IsPreorder_76 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_76
v3)))))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.Eq.refl
d_refl_172 :: T_IsBoundedJoinSemilattice_118 -> AgdaAny -> AgdaAny
d_refl_172 :: T_IsBoundedJoinSemilattice_118 -> AgdaAny -> AgdaAny
d_refl_172 T_IsBoundedJoinSemilattice_118
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsJoinSemilattice_22 -> T_IsPartialOrder_248)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> T_IsPartialOrder_248
d_isPartialOrder_30 ((T_IsBoundedJoinSemilattice_118 -> T_IsJoinSemilattice_22)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_118 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_128 (T_IsBoundedJoinSemilattice_118 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_118
v0)))))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.Eq.reflexive
d_reflexive_174 ::
  MAlonzo.Code.Agda.Primitive.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_118 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_174 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedJoinSemilattice_118
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_174 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedJoinSemilattice_118
v8
  = T_IsBoundedJoinSemilattice_118
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_174 T_IsBoundedJoinSemilattice_118
v8
du_reflexive_174 ::
  T_IsBoundedJoinSemilattice_118 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_174 :: T_IsBoundedJoinSemilattice_118
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_174 T_IsBoundedJoinSemilattice_118
v0
  = let v1 :: T_IsJoinSemilattice_22
v1 = T_IsBoundedJoinSemilattice_118 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_128 (T_IsBoundedJoinSemilattice_118 -> T_IsBoundedJoinSemilattice_118
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_118
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsJoinSemilattice_22 -> T_IsPartialOrder_248
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_76
v3
                = T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                    (T_IsPartialOrder_248 -> T_IsPartialOrder_248
forall a b. a -> b
coe T_IsPartialOrder_248
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
                    (T_IsPreorder_76 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_76
v3))
                 AgdaAny
v4)))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.Eq.sym
d_sym_176 ::
  T_IsBoundedJoinSemilattice_118 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_176 :: T_IsBoundedJoinSemilattice_118
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_176 T_IsBoundedJoinSemilattice_118
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsJoinSemilattice_22 -> T_IsPartialOrder_248)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> T_IsPartialOrder_248
d_isPartialOrder_30 ((T_IsBoundedJoinSemilattice_118 -> T_IsJoinSemilattice_22)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_118 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_128 (T_IsBoundedJoinSemilattice_118 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_118
v0)))))
-- Relation.Binary.Lattice.Structures.IsBoundedJoinSemilattice._.Eq.trans
d_trans_178 ::
  T_IsBoundedJoinSemilattice_118 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_178 :: T_IsBoundedJoinSemilattice_118
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_178 T_IsBoundedJoinSemilattice_118
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsJoinSemilattice_22 -> T_IsPartialOrder_248)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsJoinSemilattice_22 -> T_IsPartialOrder_248
d_isPartialOrder_30 ((T_IsBoundedJoinSemilattice_118 -> T_IsJoinSemilattice_22)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_118 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_128 (T_IsBoundedJoinSemilattice_118 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedJoinSemilattice_118
v0)))))
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice
d_IsMeetSemilattice_184 :: p -> p -> p -> p -> p -> p -> p -> ()
d_IsMeetSemilattice_184 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
data T_IsMeetSemilattice_184
  = C_constructor_274 MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_248
                      (AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14)
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice.isPartialOrder
d_isPartialOrder_192 ::
  T_IsMeetSemilattice_184 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_248
d_isPartialOrder_192 :: T_IsMeetSemilattice_184 -> T_IsPartialOrder_248
d_isPartialOrder_192 T_IsMeetSemilattice_184
v0
  = case T_IsMeetSemilattice_184 -> T_IsMeetSemilattice_184
forall a b. a -> b
coe T_IsMeetSemilattice_184
v0 of
      C_constructor_274 T_IsPartialOrder_248
v1 AgdaAny -> AgdaAny -> T_Σ_14
v2 -> T_IsPartialOrder_248 -> T_IsPartialOrder_248
forall a b. a -> b
coe T_IsPartialOrder_248
v1
      T_IsMeetSemilattice_184
_ -> T_IsPartialOrder_248
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice.infimum
d_infimum_194 ::
  T_IsMeetSemilattice_184 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_infimum_194 :: T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_194 T_IsMeetSemilattice_184
v0
  = case T_IsMeetSemilattice_184 -> T_IsMeetSemilattice_184
forall a b. a -> b
coe T_IsMeetSemilattice_184
v0 of
      C_constructor_274 T_IsPartialOrder_248
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_184
_ -> 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_200 ::
  MAlonzo.Code.Agda.Primitive.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_184 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'x_200 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMeetSemilattice_184
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'x_200 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsMeetSemilattice_184
v7 AgdaAny
v8 AgdaAny
v9
  = T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_200 T_IsMeetSemilattice_184
v7 AgdaAny
v8 AgdaAny
v9
du_x'8743'y'8804'x_200 ::
  T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_200 :: T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_200 T_IsMeetSemilattice_184
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_184 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_194 T_IsMeetSemilattice_184
v0 AgdaAny
v1 AgdaAny
v2)
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice.x∧y≤y
d_x'8743'y'8804'y_212 ::
  MAlonzo.Code.Agda.Primitive.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_184 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'y_212 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMeetSemilattice_184
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'y_212 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsMeetSemilattice_184
v7 AgdaAny
v8 AgdaAny
v9
  = T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_212 T_IsMeetSemilattice_184
v7 AgdaAny
v8 AgdaAny
v9
du_x'8743'y'8804'y_212 ::
  T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_212 :: T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_212 T_IsMeetSemilattice_184
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_184 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_194 T_IsMeetSemilattice_184
v0 AgdaAny
v1 AgdaAny
v2))
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice.∧-greatest
d_'8743''45'greatest_226 ::
  MAlonzo.Code.Agda.Primitive.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_184 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'greatest_226 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMeetSemilattice_184
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'greatest_226 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsMeetSemilattice_184
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
  = T_IsMeetSemilattice_184
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_226 T_IsMeetSemilattice_184
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
du_'8743''45'greatest_226 ::
  T_IsMeetSemilattice_184 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_226 :: T_IsMeetSemilattice_184
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_226 T_IsMeetSemilattice_184
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_184 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_194 T_IsMeetSemilattice_184
v0 AgdaAny
v2 AgdaAny
v3))
      AgdaAny
v1
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice._.antisym
d_antisym_238 ::
  T_IsMeetSemilattice_184 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_238 :: T_IsMeetSemilattice_184
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_238 T_IsMeetSemilattice_184
v0
  = (T_IsPartialOrder_248
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_248
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_258
      ((T_IsMeetSemilattice_184 -> T_IsPartialOrder_248)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_184 -> T_IsPartialOrder_248
d_isPartialOrder_192 (T_IsMeetSemilattice_184 -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_184
v0))
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice._.isEquivalence
d_isEquivalence_240 ::
  T_IsMeetSemilattice_184 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_240 :: T_IsMeetSemilattice_184 -> T_IsEquivalence_28
d_isEquivalence_240 T_IsMeetSemilattice_184
v0
  = (T_IsPreorder_76 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsMeetSemilattice_184 -> T_IsPartialOrder_248)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_184 -> T_IsPartialOrder_248
d_isPartialOrder_192 (T_IsMeetSemilattice_184 -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_184
v0)))
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice._.isPreorder
d_isPreorder_242 ::
  T_IsMeetSemilattice_184 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_76
d_isPreorder_242 :: T_IsMeetSemilattice_184 -> T_IsPreorder_76
d_isPreorder_242 T_IsMeetSemilattice_184
v0
  = (T_IsPartialOrder_248 -> T_IsPreorder_76)
-> AgdaAny -> T_IsPreorder_76
forall a b. a -> b
coe
      T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
      ((T_IsMeetSemilattice_184 -> T_IsPartialOrder_248)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_184 -> T_IsPartialOrder_248
d_isPartialOrder_192 (T_IsMeetSemilattice_184 -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_184
v0))
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice._.refl
d_refl_244 ::
  MAlonzo.Code.Agda.Primitive.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_184 -> AgdaAny -> AgdaAny
d_refl_244 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMeetSemilattice_184
-> AgdaAny
-> AgdaAny
d_refl_244 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsMeetSemilattice_184
v7 = T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny
du_refl_244 T_IsMeetSemilattice_184
v7
du_refl_244 :: T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny
du_refl_244 :: T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny
du_refl_244 T_IsMeetSemilattice_184
v0
  = let v1 :: T_IsPartialOrder_248
v1 = T_IsMeetSemilattice_184 -> T_IsPartialOrder_248
d_isPartialOrder_192 (T_IsMeetSemilattice_184 -> T_IsMeetSemilattice_184
forall a b. a -> b
coe T_IsMeetSemilattice_184
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsPreorder_76 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_104
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256 (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v1)))
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice._.reflexive
d_reflexive_246 ::
  T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_246 :: T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_246 T_IsMeetSemilattice_184
v0
  = (T_IsPreorder_76 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_76 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_88
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsMeetSemilattice_184 -> T_IsPartialOrder_248)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_184 -> T_IsPartialOrder_248
d_isPartialOrder_192 (T_IsMeetSemilattice_184 -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_184
v0)))
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice._.trans
d_trans_248 ::
  T_IsMeetSemilattice_184 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_248 :: T_IsMeetSemilattice_184
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_248 T_IsMeetSemilattice_184
v0
  = (T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_90
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsMeetSemilattice_184 -> T_IsPartialOrder_248)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_184 -> T_IsPartialOrder_248
d_isPartialOrder_192 (T_IsMeetSemilattice_184 -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_184
v0)))
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice._.∼-resp-≈
d_'8764''45'resp'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_184 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_250 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMeetSemilattice_184
-> T_Σ_14
d_'8764''45'resp'45''8776'_250 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsMeetSemilattice_184
v7
  = T_IsMeetSemilattice_184 -> T_Σ_14
du_'8764''45'resp'45''8776'_250 T_IsMeetSemilattice_184
v7
du_'8764''45'resp'45''8776'_250 ::
  T_IsMeetSemilattice_184 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_250 :: T_IsMeetSemilattice_184 -> T_Σ_14
du_'8764''45'resp'45''8776'_250 T_IsMeetSemilattice_184
v0
  = let v1 :: T_IsPartialOrder_248
v1 = T_IsMeetSemilattice_184 -> T_IsPartialOrder_248
d_isPartialOrder_192 (T_IsMeetSemilattice_184 -> T_IsMeetSemilattice_184
forall a b. a -> b
coe T_IsMeetSemilattice_184
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      ((T_IsPreorder_76 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_124
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256 (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v1)))
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice._.∼-respʳ-≈
d_'8764''45'resp'691''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_184 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_252 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMeetSemilattice_184
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_252 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsMeetSemilattice_184
v7
  = T_IsMeetSemilattice_184
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_252 T_IsMeetSemilattice_184
v7
du_'8764''45'resp'691''45''8776'_252 ::
  T_IsMeetSemilattice_184 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_252 :: T_IsMeetSemilattice_184
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_252 T_IsMeetSemilattice_184
v0
  = let v1 :: T_IsPartialOrder_248
v1 = T_IsMeetSemilattice_184 -> T_IsPartialOrder_248
d_isPartialOrder_192 (T_IsMeetSemilattice_184 -> T_IsMeetSemilattice_184
forall a b. a -> b
coe T_IsMeetSemilattice_184
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_122
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256 (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v1)))
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice._.∼-respˡ-≈
d_'8764''45'resp'737''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_184 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_254 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMeetSemilattice_184
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_254 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsMeetSemilattice_184
v7
  = T_IsMeetSemilattice_184
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_254 T_IsMeetSemilattice_184
v7
du_'8764''45'resp'737''45''8776'_254 ::
  T_IsMeetSemilattice_184 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_254 :: T_IsMeetSemilattice_184
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_254 T_IsMeetSemilattice_184
v0
  = let v1 :: T_IsPartialOrder_248
v1 = T_IsMeetSemilattice_184 -> T_IsPartialOrder_248
d_isPartialOrder_192 (T_IsMeetSemilattice_184 -> T_IsMeetSemilattice_184
forall a b. a -> b
coe T_IsMeetSemilattice_184
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_120
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256 (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v1)))
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice._.≲-resp-≈
d_'8818''45'resp'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_184 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8818''45'resp'45''8776'_256 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMeetSemilattice_184
-> T_Σ_14
d_'8818''45'resp'45''8776'_256 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsMeetSemilattice_184
v7
  = T_IsMeetSemilattice_184 -> T_Σ_14
du_'8818''45'resp'45''8776'_256 T_IsMeetSemilattice_184
v7
du_'8818''45'resp'45''8776'_256 ::
  T_IsMeetSemilattice_184 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8818''45'resp'45''8776'_256 :: T_IsMeetSemilattice_184 -> T_Σ_14
du_'8818''45'resp'45''8776'_256 T_IsMeetSemilattice_184
v0
  = let v1 :: T_IsPartialOrder_248
v1 = T_IsMeetSemilattice_184 -> T_IsPartialOrder_248
d_isPartialOrder_192 (T_IsMeetSemilattice_184 -> T_IsMeetSemilattice_184
forall a b. a -> b
coe T_IsMeetSemilattice_184
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      ((T_IsPreorder_76 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'45''8776'_118
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256 (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v1)))
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice._.≲-respʳ-≈
d_'8818''45'resp'691''45''8776'_258 ::
  MAlonzo.Code.Agda.Primitive.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_184 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'691''45''8776'_258 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMeetSemilattice_184
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'691''45''8776'_258 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsMeetSemilattice_184
v7
  = T_IsMeetSemilattice_184
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_258 T_IsMeetSemilattice_184
v7
du_'8818''45'resp'691''45''8776'_258 ::
  T_IsMeetSemilattice_184 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_258 :: T_IsMeetSemilattice_184
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_258 T_IsMeetSemilattice_184
v0
  = let v1 :: T_IsPartialOrder_248
v1 = T_IsMeetSemilattice_184 -> T_IsPartialOrder_248
d_isPartialOrder_192 (T_IsMeetSemilattice_184 -> T_IsMeetSemilattice_184
forall a b. a -> b
coe T_IsMeetSemilattice_184
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'691''45''8776'_112
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256 (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v1)))
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice._.≲-respˡ-≈
d_'8818''45'resp'737''45''8776'_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_184 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'737''45''8776'_260 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMeetSemilattice_184
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'737''45''8776'_260 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsMeetSemilattice_184
v7
  = T_IsMeetSemilattice_184
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_260 T_IsMeetSemilattice_184
v7
du_'8818''45'resp'737''45''8776'_260 ::
  T_IsMeetSemilattice_184 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_260 :: T_IsMeetSemilattice_184
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_260 T_IsMeetSemilattice_184
v0
  = let v1 :: T_IsPartialOrder_248
v1 = T_IsMeetSemilattice_184 -> T_IsPartialOrder_248
d_isPartialOrder_192 (T_IsMeetSemilattice_184 -> T_IsMeetSemilattice_184
forall a b. a -> b
coe T_IsMeetSemilattice_184
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'737''45''8776'_106
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256 (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v1)))
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice._.Eq.isPartialEquivalence
d_isPartialEquivalence_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_184 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_264 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMeetSemilattice_184
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_264 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsMeetSemilattice_184
v7
  = T_IsMeetSemilattice_184 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_264 T_IsMeetSemilattice_184
v7
du_isPartialEquivalence_264 ::
  T_IsMeetSemilattice_184 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_264 :: T_IsMeetSemilattice_184 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_264 T_IsMeetSemilattice_184
v0
  = let v1 :: T_IsPartialOrder_248
v1 = T_IsMeetSemilattice_184 -> T_IsPartialOrder_248
d_isPartialOrder_192 (T_IsMeetSemilattice_184 -> T_IsMeetSemilattice_184
forall a b. a -> b
coe T_IsMeetSemilattice_184
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPreorder_76
v2
             = T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                 (T_IsPartialOrder_248 -> T_IsPartialOrder_248
forall a b. a -> b
coe T_IsPartialOrder_248
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
               (T_IsPreorder_76 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_76
v2))))
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice._.Eq.refl
d_refl_266 :: T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny
d_refl_266 :: T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny
d_refl_266 T_IsMeetSemilattice_184
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsMeetSemilattice_184 -> T_IsPartialOrder_248)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_184 -> T_IsPartialOrder_248
d_isPartialOrder_192 (T_IsMeetSemilattice_184 -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_184
v0))))
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice._.Eq.reflexive
d_reflexive_268 ::
  MAlonzo.Code.Agda.Primitive.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_184 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_268 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMeetSemilattice_184
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_268 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 T_IsMeetSemilattice_184
v7
  = T_IsMeetSemilattice_184
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_268 T_IsMeetSemilattice_184
v7
du_reflexive_268 ::
  T_IsMeetSemilattice_184 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_268 :: T_IsMeetSemilattice_184
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_268 T_IsMeetSemilattice_184
v0
  = let v1 :: T_IsPartialOrder_248
v1 = T_IsMeetSemilattice_184 -> T_IsPartialOrder_248
d_isPartialOrder_192 (T_IsMeetSemilattice_184 -> T_IsMeetSemilattice_184
forall a b. a -> b
coe T_IsMeetSemilattice_184
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPreorder_76
v2
             = T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                 (T_IsPartialOrder_248 -> T_IsPartialOrder_248
forall a b. a -> b
coe T_IsPartialOrder_248
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
              ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
                 (T_IsPreorder_76 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_76
v2))
              AgdaAny
v3))
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice._.Eq.sym
d_sym_270 ::
  T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_270 :: T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_270 T_IsMeetSemilattice_184
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsMeetSemilattice_184 -> T_IsPartialOrder_248)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_184 -> T_IsPartialOrder_248
d_isPartialOrder_192 (T_IsMeetSemilattice_184 -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_184
v0))))
-- Relation.Binary.Lattice.Structures.IsMeetSemilattice._.Eq.trans
d_trans_272 ::
  T_IsMeetSemilattice_184 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_272 :: T_IsMeetSemilattice_184
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_272 T_IsMeetSemilattice_184
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsMeetSemilattice_184 -> T_IsPartialOrder_248)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_184 -> T_IsPartialOrder_248
d_isPartialOrder_192 (T_IsMeetSemilattice_184 -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_184
v0))))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice
d_IsBoundedMeetSemilattice_280 :: p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsBoundedMeetSemilattice_280 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 = ()
data T_IsBoundedMeetSemilattice_280
  = C_constructor_342 T_IsMeetSemilattice_184 (AgdaAny -> AgdaAny)
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice.isMeetSemilattice
d_isMeetSemilattice_290 ::
  T_IsBoundedMeetSemilattice_280 -> T_IsMeetSemilattice_184
d_isMeetSemilattice_290 :: T_IsBoundedMeetSemilattice_280 -> T_IsMeetSemilattice_184
d_isMeetSemilattice_290 T_IsBoundedMeetSemilattice_280
v0
  = case T_IsBoundedMeetSemilattice_280 -> T_IsBoundedMeetSemilattice_280
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_280
v0 of
      C_constructor_342 T_IsMeetSemilattice_184
v1 AgdaAny -> AgdaAny
v2 -> T_IsMeetSemilattice_184 -> T_IsMeetSemilattice_184
forall a b. a -> b
coe T_IsMeetSemilattice_184
v1
      T_IsBoundedMeetSemilattice_280
_ -> T_IsMeetSemilattice_184
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice.maximum
d_maximum_292 ::
  T_IsBoundedMeetSemilattice_280 -> AgdaAny -> AgdaAny
d_maximum_292 :: T_IsBoundedMeetSemilattice_280 -> AgdaAny -> AgdaAny
d_maximum_292 T_IsBoundedMeetSemilattice_280
v0
  = case T_IsBoundedMeetSemilattice_280 -> T_IsBoundedMeetSemilattice_280
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_280
v0 of
      C_constructor_342 T_IsMeetSemilattice_184
v1 AgdaAny -> AgdaAny
v2 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_IsBoundedMeetSemilattice_280
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.antisym
d_antisym_296 ::
  T_IsBoundedMeetSemilattice_280 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_296 :: T_IsBoundedMeetSemilattice_280
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_296 T_IsBoundedMeetSemilattice_280
v0
  = (T_IsPartialOrder_248
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_248
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_258
      ((T_IsMeetSemilattice_184 -> T_IsPartialOrder_248)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_184 -> T_IsPartialOrder_248
d_isPartialOrder_192 ((T_IsBoundedMeetSemilattice_280 -> T_IsMeetSemilattice_184)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_280 -> T_IsMeetSemilattice_184
d_isMeetSemilattice_290 (T_IsBoundedMeetSemilattice_280 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_280
v0)))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.infimum
d_infimum_298 ::
  T_IsBoundedMeetSemilattice_280 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_infimum_298 :: T_IsBoundedMeetSemilattice_280 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_298 T_IsBoundedMeetSemilattice_280
v0
  = (T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_194 ((T_IsBoundedMeetSemilattice_280 -> T_IsMeetSemilattice_184)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_280 -> T_IsMeetSemilattice_184
d_isMeetSemilattice_290 (T_IsBoundedMeetSemilattice_280 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_280
v0))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.isEquivalence
d_isEquivalence_300 ::
  T_IsBoundedMeetSemilattice_280 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_300 :: T_IsBoundedMeetSemilattice_280 -> T_IsEquivalence_28
d_isEquivalence_300 T_IsBoundedMeetSemilattice_280
v0
  = (T_IsPreorder_76 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsMeetSemilattice_184 -> T_IsPartialOrder_248)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_184 -> T_IsPartialOrder_248
d_isPartialOrder_192 ((T_IsBoundedMeetSemilattice_280 -> T_IsMeetSemilattice_184)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_280 -> T_IsMeetSemilattice_184
d_isMeetSemilattice_290 (T_IsBoundedMeetSemilattice_280 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_280
v0))))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.isPartialOrder
d_isPartialOrder_302 ::
  T_IsBoundedMeetSemilattice_280 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_248
d_isPartialOrder_302 :: T_IsBoundedMeetSemilattice_280 -> T_IsPartialOrder_248
d_isPartialOrder_302 T_IsBoundedMeetSemilattice_280
v0
  = (T_IsMeetSemilattice_184 -> T_IsPartialOrder_248)
-> AgdaAny -> T_IsPartialOrder_248
forall a b. a -> b
coe T_IsMeetSemilattice_184 -> T_IsPartialOrder_248
d_isPartialOrder_192 ((T_IsBoundedMeetSemilattice_280 -> T_IsMeetSemilattice_184)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_280 -> T_IsMeetSemilattice_184
d_isMeetSemilattice_290 (T_IsBoundedMeetSemilattice_280 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_280
v0))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.isPreorder
d_isPreorder_304 ::
  T_IsBoundedMeetSemilattice_280 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_76
d_isPreorder_304 :: T_IsBoundedMeetSemilattice_280 -> T_IsPreorder_76
d_isPreorder_304 T_IsBoundedMeetSemilattice_280
v0
  = (T_IsPartialOrder_248 -> T_IsPreorder_76)
-> AgdaAny -> T_IsPreorder_76
forall a b. a -> b
coe
      T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
      ((T_IsMeetSemilattice_184 -> T_IsPartialOrder_248)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_184 -> T_IsPartialOrder_248
d_isPartialOrder_192 ((T_IsBoundedMeetSemilattice_280 -> T_IsMeetSemilattice_184)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_280 -> T_IsMeetSemilattice_184
d_isMeetSemilattice_290 (T_IsBoundedMeetSemilattice_280 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_280
v0)))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.refl
d_refl_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_280 -> AgdaAny -> AgdaAny
d_refl_306 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedMeetSemilattice_280
-> AgdaAny
-> AgdaAny
d_refl_306 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedMeetSemilattice_280
v8 = T_IsBoundedMeetSemilattice_280 -> AgdaAny -> AgdaAny
du_refl_306 T_IsBoundedMeetSemilattice_280
v8
du_refl_306 :: T_IsBoundedMeetSemilattice_280 -> AgdaAny -> AgdaAny
du_refl_306 :: T_IsBoundedMeetSemilattice_280 -> AgdaAny -> AgdaAny
du_refl_306 T_IsBoundedMeetSemilattice_280
v0
  = let v1 :: T_IsMeetSemilattice_184
v1 = T_IsBoundedMeetSemilattice_280 -> T_IsMeetSemilattice_184
d_isMeetSemilattice_290 (T_IsBoundedMeetSemilattice_280 -> T_IsBoundedMeetSemilattice_280
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_280
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsMeetSemilattice_184 -> T_IsPartialOrder_248
d_isPartialOrder_192 (T_IsMeetSemilattice_184 -> T_IsMeetSemilattice_184
forall a b. a -> b
coe T_IsMeetSemilattice_184
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_76 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_76 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_104
            ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
               (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.reflexive
d_reflexive_308 ::
  T_IsBoundedMeetSemilattice_280 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_308 :: T_IsBoundedMeetSemilattice_280
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_308 T_IsBoundedMeetSemilattice_280
v0
  = (T_IsPreorder_76 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_76 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_88
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsMeetSemilattice_184 -> T_IsPartialOrder_248)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_184 -> T_IsPartialOrder_248
d_isPartialOrder_192 ((T_IsBoundedMeetSemilattice_280 -> T_IsMeetSemilattice_184)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_280 -> T_IsMeetSemilattice_184
d_isMeetSemilattice_290 (T_IsBoundedMeetSemilattice_280 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_280
v0))))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.trans
d_trans_310 ::
  T_IsBoundedMeetSemilattice_280 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_310 :: T_IsBoundedMeetSemilattice_280
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_310 T_IsBoundedMeetSemilattice_280
v0
  = (T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_90
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsMeetSemilattice_184 -> T_IsPartialOrder_248)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_184 -> T_IsPartialOrder_248
d_isPartialOrder_192 ((T_IsBoundedMeetSemilattice_280 -> T_IsMeetSemilattice_184)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_280 -> T_IsMeetSemilattice_184
d_isMeetSemilattice_290 (T_IsBoundedMeetSemilattice_280 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_280
v0))))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.x∧y≤x
d_x'8743'y'8804'x_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_280 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'x_312 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedMeetSemilattice_280
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'x_312 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedMeetSemilattice_280
v8
  = T_IsBoundedMeetSemilattice_280 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_312 T_IsBoundedMeetSemilattice_280
v8
du_x'8743'y'8804'x_312 ::
  T_IsBoundedMeetSemilattice_280 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_312 :: T_IsBoundedMeetSemilattice_280 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_312 T_IsBoundedMeetSemilattice_280
v0
  = (T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_200 ((T_IsBoundedMeetSemilattice_280 -> T_IsMeetSemilattice_184)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_280 -> T_IsMeetSemilattice_184
d_isMeetSemilattice_290 (T_IsBoundedMeetSemilattice_280 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_280
v0))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.x∧y≤y
d_x'8743'y'8804'y_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_280 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'y_314 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedMeetSemilattice_280
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'y_314 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedMeetSemilattice_280
v8
  = T_IsBoundedMeetSemilattice_280 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_314 T_IsBoundedMeetSemilattice_280
v8
du_x'8743'y'8804'y_314 ::
  T_IsBoundedMeetSemilattice_280 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_314 :: T_IsBoundedMeetSemilattice_280 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_314 T_IsBoundedMeetSemilattice_280
v0
  = (T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_212 ((T_IsBoundedMeetSemilattice_280 -> T_IsMeetSemilattice_184)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_280 -> T_IsMeetSemilattice_184
d_isMeetSemilattice_290 (T_IsBoundedMeetSemilattice_280 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_280
v0))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.∧-greatest
d_'8743''45'greatest_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_280 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'greatest_316 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedMeetSemilattice_280
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'greatest_316 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedMeetSemilattice_280
v8
  = T_IsBoundedMeetSemilattice_280
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_316 T_IsBoundedMeetSemilattice_280
v8
du_'8743''45'greatest_316 ::
  T_IsBoundedMeetSemilattice_280 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_316 :: T_IsBoundedMeetSemilattice_280
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_316 T_IsBoundedMeetSemilattice_280
v0
  = (T_IsMeetSemilattice_184
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMeetSemilattice_184
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_226 ((T_IsBoundedMeetSemilattice_280 -> T_IsMeetSemilattice_184)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_280 -> T_IsMeetSemilattice_184
d_isMeetSemilattice_290 (T_IsBoundedMeetSemilattice_280 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_280
v0))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.∼-resp-≈
d_'8764''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_280 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_318 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedMeetSemilattice_280
-> T_Σ_14
d_'8764''45'resp'45''8776'_318 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedMeetSemilattice_280
v8
  = T_IsBoundedMeetSemilattice_280 -> T_Σ_14
du_'8764''45'resp'45''8776'_318 T_IsBoundedMeetSemilattice_280
v8
du_'8764''45'resp'45''8776'_318 ::
  T_IsBoundedMeetSemilattice_280 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_318 :: T_IsBoundedMeetSemilattice_280 -> T_Σ_14
du_'8764''45'resp'45''8776'_318 T_IsBoundedMeetSemilattice_280
v0
  = let v1 :: T_IsMeetSemilattice_184
v1 = T_IsBoundedMeetSemilattice_280 -> T_IsMeetSemilattice_184
d_isMeetSemilattice_290 (T_IsBoundedMeetSemilattice_280 -> T_IsBoundedMeetSemilattice_280
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_280
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsMeetSemilattice_184 -> T_IsPartialOrder_248
d_isPartialOrder_192 (T_IsMeetSemilattice_184 -> T_IsMeetSemilattice_184
forall a b. a -> b
coe T_IsMeetSemilattice_184
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_76 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_76 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_124
            ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
               (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.∼-respʳ-≈
d_'8764''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_280 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_320 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedMeetSemilattice_280
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_320 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7
                                    T_IsBoundedMeetSemilattice_280
v8
  = T_IsBoundedMeetSemilattice_280
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_320 T_IsBoundedMeetSemilattice_280
v8
du_'8764''45'resp'691''45''8776'_320 ::
  T_IsBoundedMeetSemilattice_280 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_320 :: T_IsBoundedMeetSemilattice_280
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_320 T_IsBoundedMeetSemilattice_280
v0
  = let v1 :: T_IsMeetSemilattice_184
v1 = T_IsBoundedMeetSemilattice_280 -> T_IsMeetSemilattice_184
d_isMeetSemilattice_290 (T_IsBoundedMeetSemilattice_280 -> T_IsBoundedMeetSemilattice_280
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_280
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsMeetSemilattice_184 -> T_IsPartialOrder_248
d_isPartialOrder_192 (T_IsMeetSemilattice_184 -> T_IsMeetSemilattice_184
forall a b. a -> b
coe T_IsMeetSemilattice_184
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_122
            ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
               (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.∼-respˡ-≈
d_'8764''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_280 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_322 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedMeetSemilattice_280
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_322 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7
                                    T_IsBoundedMeetSemilattice_280
v8
  = T_IsBoundedMeetSemilattice_280
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_322 T_IsBoundedMeetSemilattice_280
v8
du_'8764''45'resp'737''45''8776'_322 ::
  T_IsBoundedMeetSemilattice_280 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_322 :: T_IsBoundedMeetSemilattice_280
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_322 T_IsBoundedMeetSemilattice_280
v0
  = let v1 :: T_IsMeetSemilattice_184
v1 = T_IsBoundedMeetSemilattice_280 -> T_IsMeetSemilattice_184
d_isMeetSemilattice_290 (T_IsBoundedMeetSemilattice_280 -> T_IsBoundedMeetSemilattice_280
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_280
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsMeetSemilattice_184 -> T_IsPartialOrder_248
d_isPartialOrder_192 (T_IsMeetSemilattice_184 -> T_IsMeetSemilattice_184
forall a b. a -> b
coe T_IsMeetSemilattice_184
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_120
            ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
               (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.≲-resp-≈
d_'8818''45'resp'45''8776'_324 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  T_IsBoundedMeetSemilattice_280 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8818''45'resp'45''8776'_324 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedMeetSemilattice_280
-> T_Σ_14
d_'8818''45'resp'45''8776'_324 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedMeetSemilattice_280
v8
  = T_IsBoundedMeetSemilattice_280 -> T_Σ_14
du_'8818''45'resp'45''8776'_324 T_IsBoundedMeetSemilattice_280
v8
du_'8818''45'resp'45''8776'_324 ::
  T_IsBoundedMeetSemilattice_280 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8818''45'resp'45''8776'_324 :: T_IsBoundedMeetSemilattice_280 -> T_Σ_14
du_'8818''45'resp'45''8776'_324 T_IsBoundedMeetSemilattice_280
v0
  = let v1 :: T_IsMeetSemilattice_184
v1 = T_IsBoundedMeetSemilattice_280 -> T_IsMeetSemilattice_184
d_isMeetSemilattice_290 (T_IsBoundedMeetSemilattice_280 -> T_IsBoundedMeetSemilattice_280
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_280
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsMeetSemilattice_184 -> T_IsPartialOrder_248
d_isPartialOrder_192 (T_IsMeetSemilattice_184 -> T_IsMeetSemilattice_184
forall a b. a -> b
coe T_IsMeetSemilattice_184
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_76 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_76 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'45''8776'_118
            ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
               (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.≲-respʳ-≈
d_'8818''45'resp'691''45''8776'_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_280 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'691''45''8776'_326 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedMeetSemilattice_280
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'691''45''8776'_326 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7
                                    T_IsBoundedMeetSemilattice_280
v8
  = T_IsBoundedMeetSemilattice_280
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_326 T_IsBoundedMeetSemilattice_280
v8
du_'8818''45'resp'691''45''8776'_326 ::
  T_IsBoundedMeetSemilattice_280 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_326 :: T_IsBoundedMeetSemilattice_280
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_326 T_IsBoundedMeetSemilattice_280
v0
  = let v1 :: T_IsMeetSemilattice_184
v1 = T_IsBoundedMeetSemilattice_280 -> T_IsMeetSemilattice_184
d_isMeetSemilattice_290 (T_IsBoundedMeetSemilattice_280 -> T_IsBoundedMeetSemilattice_280
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_280
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsMeetSemilattice_184 -> T_IsPartialOrder_248
d_isPartialOrder_192 (T_IsMeetSemilattice_184 -> T_IsMeetSemilattice_184
forall a b. a -> b
coe T_IsMeetSemilattice_184
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'691''45''8776'_112
            ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
               (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.≲-respˡ-≈
d_'8818''45'resp'737''45''8776'_328 ::
  MAlonzo.Code.Agda.Primitive.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_280 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'737''45''8776'_328 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedMeetSemilattice_280
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'737''45''8776'_328 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7
                                    T_IsBoundedMeetSemilattice_280
v8
  = T_IsBoundedMeetSemilattice_280
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_328 T_IsBoundedMeetSemilattice_280
v8
du_'8818''45'resp'737''45''8776'_328 ::
  T_IsBoundedMeetSemilattice_280 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_328 :: T_IsBoundedMeetSemilattice_280
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_328 T_IsBoundedMeetSemilattice_280
v0
  = let v1 :: T_IsMeetSemilattice_184
v1 = T_IsBoundedMeetSemilattice_280 -> T_IsMeetSemilattice_184
d_isMeetSemilattice_290 (T_IsBoundedMeetSemilattice_280 -> T_IsBoundedMeetSemilattice_280
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_280
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsMeetSemilattice_184 -> T_IsPartialOrder_248
d_isPartialOrder_192 (T_IsMeetSemilattice_184 -> T_IsMeetSemilattice_184
forall a b. a -> b
coe T_IsMeetSemilattice_184
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'737''45''8776'_106
            ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
               (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.Eq.isPartialEquivalence
d_isPartialEquivalence_332 ::
  MAlonzo.Code.Agda.Primitive.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_280 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_332 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedMeetSemilattice_280
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_332 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedMeetSemilattice_280
v8
  = T_IsBoundedMeetSemilattice_280 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_332 T_IsBoundedMeetSemilattice_280
v8
du_isPartialEquivalence_332 ::
  T_IsBoundedMeetSemilattice_280 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_332 :: T_IsBoundedMeetSemilattice_280 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_332 T_IsBoundedMeetSemilattice_280
v0
  = let v1 :: T_IsMeetSemilattice_184
v1 = T_IsBoundedMeetSemilattice_280 -> T_IsMeetSemilattice_184
d_isMeetSemilattice_290 (T_IsBoundedMeetSemilattice_280 -> T_IsBoundedMeetSemilattice_280
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_280
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsMeetSemilattice_184 -> T_IsPartialOrder_248
d_isPartialOrder_192 (T_IsMeetSemilattice_184 -> T_IsMeetSemilattice_184
forall a b. a -> b
coe T_IsMeetSemilattice_184
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreorder_76
v3
                = T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                    (T_IsPartialOrder_248 -> T_IsPartialOrder_248
forall a b. a -> b
coe T_IsPartialOrder_248
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
                  (T_IsPreorder_76 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_76
v3)))))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.Eq.refl
d_refl_334 :: T_IsBoundedMeetSemilattice_280 -> AgdaAny -> AgdaAny
d_refl_334 :: T_IsBoundedMeetSemilattice_280 -> AgdaAny -> AgdaAny
d_refl_334 T_IsBoundedMeetSemilattice_280
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsMeetSemilattice_184 -> T_IsPartialOrder_248)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_184 -> T_IsPartialOrder_248
d_isPartialOrder_192 ((T_IsBoundedMeetSemilattice_280 -> T_IsMeetSemilattice_184)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_280 -> T_IsMeetSemilattice_184
d_isMeetSemilattice_290 (T_IsBoundedMeetSemilattice_280 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_280
v0)))))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.Eq.reflexive
d_reflexive_336 ::
  MAlonzo.Code.Agda.Primitive.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_280 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_336 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> T_IsBoundedMeetSemilattice_280
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_336 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny
v7 T_IsBoundedMeetSemilattice_280
v8
  = T_IsBoundedMeetSemilattice_280
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_336 T_IsBoundedMeetSemilattice_280
v8
du_reflexive_336 ::
  T_IsBoundedMeetSemilattice_280 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_336 :: T_IsBoundedMeetSemilattice_280
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_336 T_IsBoundedMeetSemilattice_280
v0
  = let v1 :: T_IsMeetSemilattice_184
v1 = T_IsBoundedMeetSemilattice_280 -> T_IsMeetSemilattice_184
d_isMeetSemilattice_290 (T_IsBoundedMeetSemilattice_280 -> T_IsBoundedMeetSemilattice_280
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_280
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsMeetSemilattice_184 -> T_IsPartialOrder_248
d_isPartialOrder_192 (T_IsMeetSemilattice_184 -> T_IsMeetSemilattice_184
forall a b. a -> b
coe T_IsMeetSemilattice_184
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreorder_76
v3
                = T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                    (T_IsPartialOrder_248 -> T_IsPartialOrder_248
forall a b. a -> b
coe T_IsPartialOrder_248
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
                    (T_IsPreorder_76 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_76
v3))
                 AgdaAny
v4)))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.Eq.sym
d_sym_338 ::
  T_IsBoundedMeetSemilattice_280 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_338 :: T_IsBoundedMeetSemilattice_280
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_338 T_IsBoundedMeetSemilattice_280
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsMeetSemilattice_184 -> T_IsPartialOrder_248)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_184 -> T_IsPartialOrder_248
d_isPartialOrder_192 ((T_IsBoundedMeetSemilattice_280 -> T_IsMeetSemilattice_184)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_280 -> T_IsMeetSemilattice_184
d_isMeetSemilattice_290 (T_IsBoundedMeetSemilattice_280 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_280
v0)))))
-- Relation.Binary.Lattice.Structures.IsBoundedMeetSemilattice._.Eq.trans
d_trans_340 ::
  T_IsBoundedMeetSemilattice_280 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_340 :: T_IsBoundedMeetSemilattice_280
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_340 T_IsBoundedMeetSemilattice_280
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsMeetSemilattice_184 -> T_IsPartialOrder_248)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsMeetSemilattice_184 -> T_IsPartialOrder_248
d_isPartialOrder_192 ((T_IsBoundedMeetSemilattice_280 -> T_IsMeetSemilattice_184)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_280 -> T_IsMeetSemilattice_184
d_isMeetSemilattice_290 (T_IsBoundedMeetSemilattice_280 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedMeetSemilattice_280
v0)))))
-- Relation.Binary.Lattice.Structures.IsLattice
d_IsLattice_348 :: p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsLattice_348 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 = ()
data T_IsLattice_348
  = C_constructor_424 MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_248
                      (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_360 ::
  T_IsLattice_348 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_248
d_isPartialOrder_360 :: T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 T_IsLattice_348
v0
  = case T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v0 of
      C_constructor_424 T_IsPartialOrder_248
v1 AgdaAny -> AgdaAny -> T_Σ_14
v2 AgdaAny -> AgdaAny -> T_Σ_14
v3 -> T_IsPartialOrder_248 -> T_IsPartialOrder_248
forall a b. a -> b
coe T_IsPartialOrder_248
v1
      T_IsLattice_348
_ -> T_IsPartialOrder_248
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.Structures.IsLattice.supremum
d_supremum_362 ::
  T_IsLattice_348 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_supremum_362 :: T_IsLattice_348 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_362 T_IsLattice_348
v0
  = case T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v0 of
      C_constructor_424 T_IsPartialOrder_248
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_348
_ -> AgdaAny -> AgdaAny -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.Structures.IsLattice.infimum
d_infimum_364 ::
  T_IsLattice_348 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_infimum_364 :: T_IsLattice_348 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_364 T_IsLattice_348
v0
  = case T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v0 of
      C_constructor_424 T_IsPartialOrder_248
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_348
_ -> AgdaAny -> AgdaAny -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.Structures.IsLattice.isJoinSemilattice
d_isJoinSemilattice_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_348 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_366 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_348
-> T_IsJoinSemilattice_22
d_isJoinSemilattice_366 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsLattice_348
v8
  = T_IsLattice_348 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_366 T_IsLattice_348
v8
du_isJoinSemilattice_366 ::
  T_IsLattice_348 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_366 :: T_IsLattice_348 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_366 T_IsLattice_348
v0
  = (T_IsPartialOrder_248
 -> (AgdaAny -> AgdaAny -> T_Σ_14) -> T_IsJoinSemilattice_22)
-> AgdaAny -> AgdaAny -> T_IsJoinSemilattice_22
forall a b. a -> b
coe
      T_IsPartialOrder_248
-> (AgdaAny -> AgdaAny -> T_Σ_14) -> T_IsJoinSemilattice_22
C_constructor_112 ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v0))
      ((T_IsLattice_348 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_362 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v0))
-- Relation.Binary.Lattice.Structures.IsLattice.isMeetSemilattice
d_isMeetSemilattice_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_348 -> T_IsMeetSemilattice_184
d_isMeetSemilattice_368 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_348
-> T_IsMeetSemilattice_184
d_isMeetSemilattice_368 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsLattice_348
v8
  = T_IsLattice_348 -> T_IsMeetSemilattice_184
du_isMeetSemilattice_368 T_IsLattice_348
v8
du_isMeetSemilattice_368 ::
  T_IsLattice_348 -> T_IsMeetSemilattice_184
du_isMeetSemilattice_368 :: T_IsLattice_348 -> T_IsMeetSemilattice_184
du_isMeetSemilattice_368 T_IsLattice_348
v0
  = (T_IsPartialOrder_248
 -> (AgdaAny -> AgdaAny -> T_Σ_14) -> T_IsMeetSemilattice_184)
-> AgdaAny -> AgdaAny -> T_IsMeetSemilattice_184
forall a b. a -> b
coe
      T_IsPartialOrder_248
-> (AgdaAny -> AgdaAny -> T_Σ_14) -> T_IsMeetSemilattice_184
C_constructor_274 ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v0))
      ((T_IsLattice_348 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_364 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v0))
-- Relation.Binary.Lattice.Structures.IsLattice._.x≤x∨y
d_x'8804'x'8744'y_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_348 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8804'x'8744'y_372 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_348
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8804'x'8744'y_372 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsLattice_348
v8
  = T_IsLattice_348 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_372 T_IsLattice_348
v8
du_x'8804'x'8744'y_372 ::
  T_IsLattice_348 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_372 :: T_IsLattice_348 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_372 T_IsLattice_348
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_348 -> T_IsJoinSemilattice_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_366 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v0))
-- Relation.Binary.Lattice.Structures.IsLattice._.y≤x∨y
d_y'8804'x'8744'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_348 -> AgdaAny -> AgdaAny -> AgdaAny
d_y'8804'x'8744'y_374 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_348
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_y'8804'x'8744'y_374 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsLattice_348
v8
  = T_IsLattice_348 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_374 T_IsLattice_348
v8
du_y'8804'x'8744'y_374 ::
  T_IsLattice_348 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_374 :: T_IsLattice_348 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_374 T_IsLattice_348
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_348 -> T_IsJoinSemilattice_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_366 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v0))
-- Relation.Binary.Lattice.Structures.IsLattice._.∨-least
d_'8744''45'least_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_348 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'least_376 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_348
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'least_376 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsLattice_348
v8
  = T_IsLattice_348
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_376 T_IsLattice_348
v8
du_'8744''45'least_376 ::
  T_IsLattice_348 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_376 :: T_IsLattice_348
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_376 T_IsLattice_348
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_348 -> T_IsJoinSemilattice_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_366 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v0))
-- Relation.Binary.Lattice.Structures.IsLattice._.x∧y≤x
d_x'8743'y'8804'x_380 ::
  MAlonzo.Code.Agda.Primitive.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_348 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'x_380 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_348
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'x_380 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsLattice_348
v8
  = T_IsLattice_348 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_380 T_IsLattice_348
v8
du_x'8743'y'8804'x_380 ::
  T_IsLattice_348 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_380 :: T_IsLattice_348 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_380 T_IsLattice_348
v0
  = (T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_200 ((T_IsLattice_348 -> T_IsMeetSemilattice_184) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsMeetSemilattice_184
du_isMeetSemilattice_368 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v0))
-- Relation.Binary.Lattice.Structures.IsLattice._.x∧y≤y
d_x'8743'y'8804'y_382 ::
  MAlonzo.Code.Agda.Primitive.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_348 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'y_382 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_348
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'y_382 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsLattice_348
v8
  = T_IsLattice_348 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_382 T_IsLattice_348
v8
du_x'8743'y'8804'y_382 ::
  T_IsLattice_348 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_382 :: T_IsLattice_348 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_382 T_IsLattice_348
v0
  = (T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_212 ((T_IsLattice_348 -> T_IsMeetSemilattice_184) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsMeetSemilattice_184
du_isMeetSemilattice_368 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v0))
-- Relation.Binary.Lattice.Structures.IsLattice._.∧-greatest
d_'8743''45'greatest_384 ::
  MAlonzo.Code.Agda.Primitive.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_348 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'greatest_384 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_348
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'greatest_384 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsLattice_348
v8
  = T_IsLattice_348
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_384 T_IsLattice_348
v8
du_'8743''45'greatest_384 ::
  T_IsLattice_348 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_384 :: T_IsLattice_348
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_384 T_IsLattice_348
v0
  = (T_IsMeetSemilattice_184
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsMeetSemilattice_184
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_226 ((T_IsLattice_348 -> T_IsMeetSemilattice_184) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsMeetSemilattice_184
du_isMeetSemilattice_368 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v0))
-- Relation.Binary.Lattice.Structures.IsLattice._.antisym
d_antisym_388 ::
  T_IsLattice_348 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_388 :: T_IsLattice_348
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_388 T_IsLattice_348
v0
  = (T_IsPartialOrder_248
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_248
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_258
      ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v0))
-- Relation.Binary.Lattice.Structures.IsLattice._.isEquivalence
d_isEquivalence_390 ::
  T_IsLattice_348 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_390 :: T_IsLattice_348 -> T_IsEquivalence_28
d_isEquivalence_390 T_IsLattice_348
v0
  = (T_IsPreorder_76 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v0)))
-- Relation.Binary.Lattice.Structures.IsLattice._.isPreorder
d_isPreorder_392 ::
  T_IsLattice_348 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_76
d_isPreorder_392 :: T_IsLattice_348 -> T_IsPreorder_76
d_isPreorder_392 T_IsLattice_348
v0
  = (T_IsPartialOrder_248 -> T_IsPreorder_76)
-> AgdaAny -> T_IsPreorder_76
forall a b. a -> b
coe
      T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
      ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v0))
-- Relation.Binary.Lattice.Structures.IsLattice._.refl
d_refl_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_348 -> AgdaAny -> AgdaAny
d_refl_394 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_348
-> AgdaAny
-> AgdaAny
d_refl_394 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsLattice_348
v8 = T_IsLattice_348 -> AgdaAny -> AgdaAny
du_refl_394 T_IsLattice_348
v8
du_refl_394 :: T_IsLattice_348 -> AgdaAny -> AgdaAny
du_refl_394 :: T_IsLattice_348 -> AgdaAny -> AgdaAny
du_refl_394 T_IsLattice_348
v0
  = let v1 :: T_IsPartialOrder_248
v1 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsPreorder_76 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_104
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256 (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v1)))
-- Relation.Binary.Lattice.Structures.IsLattice._.reflexive
d_reflexive_396 ::
  T_IsLattice_348 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_396 :: T_IsLattice_348 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_396 T_IsLattice_348
v0
  = (T_IsPreorder_76 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_76 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_88
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v0)))
-- Relation.Binary.Lattice.Structures.IsLattice._.trans
d_trans_398 ::
  T_IsLattice_348 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_398 :: T_IsLattice_348
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_398 T_IsLattice_348
v0
  = (T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_90
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v0)))
-- Relation.Binary.Lattice.Structures.IsLattice._.∼-resp-≈
d_'8764''45'resp'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_348 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_400 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_348
-> T_Σ_14
d_'8764''45'resp'45''8776'_400 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsLattice_348
v8
  = T_IsLattice_348 -> T_Σ_14
du_'8764''45'resp'45''8776'_400 T_IsLattice_348
v8
du_'8764''45'resp'45''8776'_400 ::
  T_IsLattice_348 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_400 :: T_IsLattice_348 -> T_Σ_14
du_'8764''45'resp'45''8776'_400 T_IsLattice_348
v0
  = let v1 :: T_IsPartialOrder_248
v1 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      ((T_IsPreorder_76 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_124
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256 (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v1)))
-- Relation.Binary.Lattice.Structures.IsLattice._.∼-respʳ-≈
d_'8764''45'resp'691''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_348 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_402 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_348
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_402 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7
                                    T_IsLattice_348
v8
  = T_IsLattice_348
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_402 T_IsLattice_348
v8
du_'8764''45'resp'691''45''8776'_402 ::
  T_IsLattice_348 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_402 :: T_IsLattice_348
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_402 T_IsLattice_348
v0
  = let v1 :: T_IsPartialOrder_248
v1 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_122
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256 (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v1)))
-- Relation.Binary.Lattice.Structures.IsLattice._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_404 ::
  MAlonzo.Code.Agda.Primitive.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_348 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_404 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_348
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_404 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7
                                    T_IsLattice_348
v8
  = T_IsLattice_348
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_404 T_IsLattice_348
v8
du_'8764''45'resp'737''45''8776'_404 ::
  T_IsLattice_348 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_404 :: T_IsLattice_348
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_404 T_IsLattice_348
v0
  = let v1 :: T_IsPartialOrder_248
v1 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_120
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256 (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v1)))
-- Relation.Binary.Lattice.Structures.IsLattice._.≲-resp-≈
d_'8818''45'resp'45''8776'_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_348 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8818''45'resp'45''8776'_406 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_348
-> T_Σ_14
d_'8818''45'resp'45''8776'_406 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsLattice_348
v8
  = T_IsLattice_348 -> T_Σ_14
du_'8818''45'resp'45''8776'_406 T_IsLattice_348
v8
du_'8818''45'resp'45''8776'_406 ::
  T_IsLattice_348 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8818''45'resp'45''8776'_406 :: T_IsLattice_348 -> T_Σ_14
du_'8818''45'resp'45''8776'_406 T_IsLattice_348
v0
  = let v1 :: T_IsPartialOrder_248
v1 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      ((T_IsPreorder_76 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'45''8776'_118
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256 (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v1)))
-- Relation.Binary.Lattice.Structures.IsLattice._.≲-respʳ-≈
d_'8818''45'resp'691''45''8776'_408 ::
  MAlonzo.Code.Agda.Primitive.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_348 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'691''45''8776'_408 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_348
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'691''45''8776'_408 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7
                                    T_IsLattice_348
v8
  = T_IsLattice_348
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_408 T_IsLattice_348
v8
du_'8818''45'resp'691''45''8776'_408 ::
  T_IsLattice_348 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_408 :: T_IsLattice_348
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_408 T_IsLattice_348
v0
  = let v1 :: T_IsPartialOrder_248
v1 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'691''45''8776'_112
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256 (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v1)))
-- Relation.Binary.Lattice.Structures.IsLattice._.≲-respˡ-≈
d_'8818''45'resp'737''45''8776'_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_348 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'737''45''8776'_410 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_348
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'737''45''8776'_410 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7
                                    T_IsLattice_348
v8
  = T_IsLattice_348
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_410 T_IsLattice_348
v8
du_'8818''45'resp'737''45''8776'_410 ::
  T_IsLattice_348 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_410 :: T_IsLattice_348
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_410 T_IsLattice_348
v0
  = let v1 :: T_IsPartialOrder_248
v1 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'737''45''8776'_106
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256 (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v1)))
-- Relation.Binary.Lattice.Structures.IsLattice._.Eq.isPartialEquivalence
d_isPartialEquivalence_414 ::
  MAlonzo.Code.Agda.Primitive.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_348 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_414 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_348
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_414 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsLattice_348
v8
  = T_IsLattice_348 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_414 T_IsLattice_348
v8
du_isPartialEquivalence_414 ::
  T_IsLattice_348 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_414 :: T_IsLattice_348 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_414 T_IsLattice_348
v0
  = let v1 :: T_IsPartialOrder_248
v1 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPreorder_76
v2
             = T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                 (T_IsPartialOrder_248 -> T_IsPartialOrder_248
forall a b. a -> b
coe T_IsPartialOrder_248
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
            ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
               (T_IsPreorder_76 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_76
v2))))
-- Relation.Binary.Lattice.Structures.IsLattice._.Eq.refl
d_refl_416 :: T_IsLattice_348 -> AgdaAny -> AgdaAny
d_refl_416 :: T_IsLattice_348 -> AgdaAny -> AgdaAny
d_refl_416 T_IsLattice_348
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v0))))
-- Relation.Binary.Lattice.Structures.IsLattice._.Eq.reflexive
d_reflexive_418 ::
  MAlonzo.Code.Agda.Primitive.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_348 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_418 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_348
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_418 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsLattice_348
v8
  = T_IsLattice_348 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_418 T_IsLattice_348
v8
du_reflexive_418 ::
  T_IsLattice_348 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_418 :: T_IsLattice_348 -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_418 T_IsLattice_348
v0
  = let v1 :: T_IsPartialOrder_248
v1 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPreorder_76
v2
             = T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                 (T_IsPartialOrder_248 -> T_IsPartialOrder_248
forall a b. a -> b
coe T_IsPartialOrder_248
v1) in
       (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
              ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
                 (T_IsPreorder_76 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_76
v2))
              AgdaAny
v3))
-- Relation.Binary.Lattice.Structures.IsLattice._.Eq.sym
d_sym_420 ::
  T_IsLattice_348 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_420 :: T_IsLattice_348 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_420 T_IsLattice_348
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v0))))
-- Relation.Binary.Lattice.Structures.IsLattice._.Eq.trans
d_trans_422 ::
  T_IsLattice_348 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_422 :: T_IsLattice_348
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_422 T_IsLattice_348
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v0))))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice
d_IsDistributiveLattice_430 :: p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsDistributiveLattice_430 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 = ()
data T_IsDistributiveLattice_430
  = C_constructor_504 T_IsLattice_348
                      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice.isLattice
d_isLattice_440 :: T_IsDistributiveLattice_430 -> T_IsLattice_348
d_isLattice_440 :: T_IsDistributiveLattice_430 -> T_IsLattice_348
d_isLattice_440 T_IsDistributiveLattice_430
v0
  = case T_IsDistributiveLattice_430 -> T_IsDistributiveLattice_430
forall a b. a -> b
coe T_IsDistributiveLattice_430
v0 of
      C_constructor_504 T_IsLattice_348
v1 AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
v2 -> T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v1
      T_IsDistributiveLattice_430
_ -> T_IsLattice_348
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice.∧-distribˡ-∨
d_'8743''45'distrib'737''45''8744'_442 ::
  T_IsDistributiveLattice_430 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'distrib'737''45''8744'_442 :: T_IsDistributiveLattice_430
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'distrib'737''45''8744'_442 T_IsDistributiveLattice_430
v0
  = case T_IsDistributiveLattice_430 -> T_IsDistributiveLattice_430
forall a b. a -> b
coe T_IsDistributiveLattice_430
v0 of
      C_constructor_504 T_IsLattice_348
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_430
_ -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.antisym
d_antisym_446 ::
  T_IsDistributiveLattice_430 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_446 :: T_IsDistributiveLattice_430
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_446 T_IsDistributiveLattice_430
v0
  = (T_IsPartialOrder_248
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_248
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_258
      ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 ((T_IsDistributiveLattice_430 -> T_IsLattice_348)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_430 -> T_IsLattice_348
d_isLattice_440 (T_IsDistributiveLattice_430 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_430
v0)))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.infimum
d_infimum_448 ::
  T_IsDistributiveLattice_430 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_infimum_448 :: T_IsDistributiveLattice_430 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_448 T_IsDistributiveLattice_430
v0 = (T_IsLattice_348 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsLattice_348 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_364 ((T_IsDistributiveLattice_430 -> T_IsLattice_348)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_430 -> T_IsLattice_348
d_isLattice_440 (T_IsDistributiveLattice_430 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_430
v0))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.isEquivalence
d_isEquivalence_450 ::
  T_IsDistributiveLattice_430 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_450 :: T_IsDistributiveLattice_430 -> T_IsEquivalence_28
d_isEquivalence_450 T_IsDistributiveLattice_430
v0
  = (T_IsPreorder_76 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 ((T_IsDistributiveLattice_430 -> T_IsLattice_348)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_430 -> T_IsLattice_348
d_isLattice_440 (T_IsDistributiveLattice_430 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_430
v0))))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.isJoinSemilattice
d_isJoinSemilattice_452 ::
  MAlonzo.Code.Agda.Primitive.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_430 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_452 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_430
-> T_IsJoinSemilattice_22
d_isJoinSemilattice_452 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsDistributiveLattice_430
v8
  = T_IsDistributiveLattice_430 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_452 T_IsDistributiveLattice_430
v8
du_isJoinSemilattice_452 ::
  T_IsDistributiveLattice_430 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_452 :: T_IsDistributiveLattice_430 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_452 T_IsDistributiveLattice_430
v0
  = (T_IsLattice_348 -> T_IsJoinSemilattice_22)
-> AgdaAny -> T_IsJoinSemilattice_22
forall a b. a -> b
coe T_IsLattice_348 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_366 ((T_IsDistributiveLattice_430 -> T_IsLattice_348)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_430 -> T_IsLattice_348
d_isLattice_440 (T_IsDistributiveLattice_430 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_430
v0))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.isMeetSemilattice
d_isMeetSemilattice_454 ::
  MAlonzo.Code.Agda.Primitive.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_430 -> T_IsMeetSemilattice_184
d_isMeetSemilattice_454 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_430
-> T_IsMeetSemilattice_184
d_isMeetSemilattice_454 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsDistributiveLattice_430
v8
  = T_IsDistributiveLattice_430 -> T_IsMeetSemilattice_184
du_isMeetSemilattice_454 T_IsDistributiveLattice_430
v8
du_isMeetSemilattice_454 ::
  T_IsDistributiveLattice_430 -> T_IsMeetSemilattice_184
du_isMeetSemilattice_454 :: T_IsDistributiveLattice_430 -> T_IsMeetSemilattice_184
du_isMeetSemilattice_454 T_IsDistributiveLattice_430
v0
  = (T_IsLattice_348 -> T_IsMeetSemilattice_184)
-> AgdaAny -> T_IsMeetSemilattice_184
forall a b. a -> b
coe T_IsLattice_348 -> T_IsMeetSemilattice_184
du_isMeetSemilattice_368 ((T_IsDistributiveLattice_430 -> T_IsLattice_348)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_430 -> T_IsLattice_348
d_isLattice_440 (T_IsDistributiveLattice_430 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_430
v0))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.isPartialOrder
d_isPartialOrder_456 ::
  T_IsDistributiveLattice_430 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_248
d_isPartialOrder_456 :: T_IsDistributiveLattice_430 -> T_IsPartialOrder_248
d_isPartialOrder_456 T_IsDistributiveLattice_430
v0
  = (T_IsLattice_348 -> T_IsPartialOrder_248)
-> AgdaAny -> T_IsPartialOrder_248
forall a b. a -> b
coe T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 ((T_IsDistributiveLattice_430 -> T_IsLattice_348)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_430 -> T_IsLattice_348
d_isLattice_440 (T_IsDistributiveLattice_430 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_430
v0))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.isPreorder
d_isPreorder_458 ::
  T_IsDistributiveLattice_430 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_76
d_isPreorder_458 :: T_IsDistributiveLattice_430 -> T_IsPreorder_76
d_isPreorder_458 T_IsDistributiveLattice_430
v0
  = (T_IsPartialOrder_248 -> T_IsPreorder_76)
-> AgdaAny -> T_IsPreorder_76
forall a b. a -> b
coe
      T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
      ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 ((T_IsDistributiveLattice_430 -> T_IsLattice_348)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_430 -> T_IsLattice_348
d_isLattice_440 (T_IsDistributiveLattice_430 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_430
v0)))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.refl
d_refl_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_430 -> AgdaAny -> AgdaAny
d_refl_460 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_430
-> AgdaAny
-> AgdaAny
d_refl_460 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsDistributiveLattice_430
v8 = T_IsDistributiveLattice_430 -> AgdaAny -> AgdaAny
du_refl_460 T_IsDistributiveLattice_430
v8
du_refl_460 :: T_IsDistributiveLattice_430 -> AgdaAny -> AgdaAny
du_refl_460 :: T_IsDistributiveLattice_430 -> AgdaAny -> AgdaAny
du_refl_460 T_IsDistributiveLattice_430
v0
  = let v1 :: T_IsLattice_348
v1 = T_IsDistributiveLattice_430 -> T_IsLattice_348
d_isLattice_440 (T_IsDistributiveLattice_430 -> T_IsDistributiveLattice_430
forall a b. a -> b
coe T_IsDistributiveLattice_430
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_76 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_76 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_104
            ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
               (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v2))))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.reflexive
d_reflexive_462 ::
  T_IsDistributiveLattice_430 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_462 :: T_IsDistributiveLattice_430
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_462 T_IsDistributiveLattice_430
v0
  = (T_IsPreorder_76 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_76 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_88
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 ((T_IsDistributiveLattice_430 -> T_IsLattice_348)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_430 -> T_IsLattice_348
d_isLattice_440 (T_IsDistributiveLattice_430 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_430
v0))))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.supremum
d_supremum_464 ::
  T_IsDistributiveLattice_430 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_supremum_464 :: T_IsDistributiveLattice_430 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_464 T_IsDistributiveLattice_430
v0
  = (T_IsLattice_348 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsLattice_348 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_362 ((T_IsDistributiveLattice_430 -> T_IsLattice_348)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_430 -> T_IsLattice_348
d_isLattice_440 (T_IsDistributiveLattice_430 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_430
v0))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.trans
d_trans_466 ::
  T_IsDistributiveLattice_430 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_466 :: T_IsDistributiveLattice_430
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_466 T_IsDistributiveLattice_430
v0
  = (T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_90
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 ((T_IsDistributiveLattice_430 -> T_IsLattice_348)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_430 -> T_IsLattice_348
d_isLattice_440 (T_IsDistributiveLattice_430 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_430
v0))))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.x∧y≤x
d_x'8743'y'8804'x_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_430 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'x_468 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_430
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'x_468 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsDistributiveLattice_430
v8
  = T_IsDistributiveLattice_430 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_468 T_IsDistributiveLattice_430
v8
du_x'8743'y'8804'x_468 ::
  T_IsDistributiveLattice_430 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_468 :: T_IsDistributiveLattice_430 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_468 T_IsDistributiveLattice_430
v0
  = let v1 :: T_IsLattice_348
v1 = T_IsDistributiveLattice_430 -> T_IsLattice_348
d_isLattice_440 (T_IsDistributiveLattice_430 -> T_IsDistributiveLattice_430
forall a b. a -> b
coe T_IsDistributiveLattice_430
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_200 ((T_IsLattice_348 -> T_IsMeetSemilattice_184) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsMeetSemilattice_184
du_isMeetSemilattice_368 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v1)))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.x∧y≤y
d_x'8743'y'8804'y_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_430 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'y_470 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_430
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'y_470 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsDistributiveLattice_430
v8
  = T_IsDistributiveLattice_430 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_470 T_IsDistributiveLattice_430
v8
du_x'8743'y'8804'y_470 ::
  T_IsDistributiveLattice_430 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_470 :: T_IsDistributiveLattice_430 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_470 T_IsDistributiveLattice_430
v0
  = let v1 :: T_IsLattice_348
v1 = T_IsDistributiveLattice_430 -> T_IsLattice_348
d_isLattice_440 (T_IsDistributiveLattice_430 -> T_IsDistributiveLattice_430
forall a b. a -> b
coe T_IsDistributiveLattice_430
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_212 ((T_IsLattice_348 -> T_IsMeetSemilattice_184) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsMeetSemilattice_184
du_isMeetSemilattice_368 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v1)))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.x≤x∨y
d_x'8804'x'8744'y_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_430 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8804'x'8744'y_472 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_430
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8804'x'8744'y_472 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsDistributiveLattice_430
v8
  = T_IsDistributiveLattice_430 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_472 T_IsDistributiveLattice_430
v8
du_x'8804'x'8744'y_472 ::
  T_IsDistributiveLattice_430 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_472 :: T_IsDistributiveLattice_430 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_472 T_IsDistributiveLattice_430
v0
  = let v1 :: T_IsLattice_348
v1 = T_IsDistributiveLattice_430 -> T_IsLattice_348
d_isLattice_440 (T_IsDistributiveLattice_430 -> T_IsDistributiveLattice_430
forall a b. a -> b
coe T_IsDistributiveLattice_430
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_348 -> T_IsJoinSemilattice_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_366 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v1)))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.y≤x∨y
d_y'8804'x'8744'y_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_430 -> AgdaAny -> AgdaAny -> AgdaAny
d_y'8804'x'8744'y_474 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_430
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_y'8804'x'8744'y_474 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsDistributiveLattice_430
v8
  = T_IsDistributiveLattice_430 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_474 T_IsDistributiveLattice_430
v8
du_y'8804'x'8744'y_474 ::
  T_IsDistributiveLattice_430 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_474 :: T_IsDistributiveLattice_430 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_474 T_IsDistributiveLattice_430
v0
  = let v1 :: T_IsLattice_348
v1 = T_IsDistributiveLattice_430 -> T_IsLattice_348
d_isLattice_440 (T_IsDistributiveLattice_430 -> T_IsDistributiveLattice_430
forall a b. a -> b
coe T_IsDistributiveLattice_430
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_348 -> T_IsJoinSemilattice_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_366 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v1)))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.∧-greatest
d_'8743''45'greatest_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_430 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'greatest_476 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_430
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'greatest_476 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsDistributiveLattice_430
v8
  = T_IsDistributiveLattice_430
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_476 T_IsDistributiveLattice_430
v8
du_'8743''45'greatest_476 ::
  T_IsDistributiveLattice_430 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_476 :: T_IsDistributiveLattice_430
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_476 T_IsDistributiveLattice_430
v0
  = let v1 :: T_IsLattice_348
v1 = T_IsDistributiveLattice_430 -> T_IsLattice_348
d_isLattice_440 (T_IsDistributiveLattice_430 -> T_IsDistributiveLattice_430
forall a b. a -> b
coe T_IsDistributiveLattice_430
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMeetSemilattice_184
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMeetSemilattice_184
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_226 ((T_IsLattice_348 -> T_IsMeetSemilattice_184) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsMeetSemilattice_184
du_isMeetSemilattice_368 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v1)))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.∨-least
d_'8744''45'least_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_430 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'least_478 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_430
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'least_478 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsDistributiveLattice_430
v8
  = T_IsDistributiveLattice_430
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_478 T_IsDistributiveLattice_430
v8
du_'8744''45'least_478 ::
  T_IsDistributiveLattice_430 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_478 :: T_IsDistributiveLattice_430
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_478 T_IsDistributiveLattice_430
v0
  = let v1 :: T_IsLattice_348
v1 = T_IsDistributiveLattice_430 -> T_IsLattice_348
d_isLattice_440 (T_IsDistributiveLattice_430 -> T_IsDistributiveLattice_430
forall a b. a -> b
coe T_IsDistributiveLattice_430
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_348 -> T_IsJoinSemilattice_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_366 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v1)))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.∼-resp-≈
d_'8764''45'resp'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_430 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_480 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_430
-> T_Σ_14
d_'8764''45'resp'45''8776'_480 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsDistributiveLattice_430
v8
  = T_IsDistributiveLattice_430 -> T_Σ_14
du_'8764''45'resp'45''8776'_480 T_IsDistributiveLattice_430
v8
du_'8764''45'resp'45''8776'_480 ::
  T_IsDistributiveLattice_430 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_480 :: T_IsDistributiveLattice_430 -> T_Σ_14
du_'8764''45'resp'45''8776'_480 T_IsDistributiveLattice_430
v0
  = let v1 :: T_IsLattice_348
v1 = T_IsDistributiveLattice_430 -> T_IsLattice_348
d_isLattice_440 (T_IsDistributiveLattice_430 -> T_IsDistributiveLattice_430
forall a b. a -> b
coe T_IsDistributiveLattice_430
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_76 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_76 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_124
            ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
               (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v2))))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_482 ::
  MAlonzo.Code.Agda.Primitive.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_430 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_482 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_430
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_482 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7
                                    T_IsDistributiveLattice_430
v8
  = T_IsDistributiveLattice_430
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_482 T_IsDistributiveLattice_430
v8
du_'8764''45'resp'691''45''8776'_482 ::
  T_IsDistributiveLattice_430 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_482 :: T_IsDistributiveLattice_430
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_482 T_IsDistributiveLattice_430
v0
  = let v1 :: T_IsLattice_348
v1 = T_IsDistributiveLattice_430 -> T_IsLattice_348
d_isLattice_440 (T_IsDistributiveLattice_430 -> T_IsDistributiveLattice_430
forall a b. a -> b
coe T_IsDistributiveLattice_430
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_122
            ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
               (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v2))))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_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_430 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_484 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_430
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_484 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7
                                    T_IsDistributiveLattice_430
v8
  = T_IsDistributiveLattice_430
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_484 T_IsDistributiveLattice_430
v8
du_'8764''45'resp'737''45''8776'_484 ::
  T_IsDistributiveLattice_430 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_484 :: T_IsDistributiveLattice_430
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_484 T_IsDistributiveLattice_430
v0
  = let v1 :: T_IsLattice_348
v1 = T_IsDistributiveLattice_430 -> T_IsLattice_348
d_isLattice_440 (T_IsDistributiveLattice_430 -> T_IsDistributiveLattice_430
forall a b. a -> b
coe T_IsDistributiveLattice_430
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_120
            ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
               (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v2))))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.≲-resp-≈
d_'8818''45'resp'45''8776'_486 ::
  MAlonzo.Code.Agda.Primitive.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_430 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8818''45'resp'45''8776'_486 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_430
-> T_Σ_14
d_'8818''45'resp'45''8776'_486 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsDistributiveLattice_430
v8
  = T_IsDistributiveLattice_430 -> T_Σ_14
du_'8818''45'resp'45''8776'_486 T_IsDistributiveLattice_430
v8
du_'8818''45'resp'45''8776'_486 ::
  T_IsDistributiveLattice_430 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8818''45'resp'45''8776'_486 :: T_IsDistributiveLattice_430 -> T_Σ_14
du_'8818''45'resp'45''8776'_486 T_IsDistributiveLattice_430
v0
  = let v1 :: T_IsLattice_348
v1 = T_IsDistributiveLattice_430 -> T_IsLattice_348
d_isLattice_440 (T_IsDistributiveLattice_430 -> T_IsDistributiveLattice_430
forall a b. a -> b
coe T_IsDistributiveLattice_430
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_76 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_76 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'45''8776'_118
            ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
               (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v2))))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.≲-respʳ-≈
d_'8818''45'resp'691''45''8776'_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_430 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'691''45''8776'_488 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_430
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'691''45''8776'_488 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7
                                    T_IsDistributiveLattice_430
v8
  = T_IsDistributiveLattice_430
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_488 T_IsDistributiveLattice_430
v8
du_'8818''45'resp'691''45''8776'_488 ::
  T_IsDistributiveLattice_430 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_488 :: T_IsDistributiveLattice_430
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_488 T_IsDistributiveLattice_430
v0
  = let v1 :: T_IsLattice_348
v1 = T_IsDistributiveLattice_430 -> T_IsLattice_348
d_isLattice_440 (T_IsDistributiveLattice_430 -> T_IsDistributiveLattice_430
forall a b. a -> b
coe T_IsDistributiveLattice_430
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'691''45''8776'_112
            ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
               (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v2))))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.≲-respˡ-≈
d_'8818''45'resp'737''45''8776'_490 ::
  MAlonzo.Code.Agda.Primitive.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_430 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'737''45''8776'_490 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_430
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'737''45''8776'_490 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7
                                    T_IsDistributiveLattice_430
v8
  = T_IsDistributiveLattice_430
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_490 T_IsDistributiveLattice_430
v8
du_'8818''45'resp'737''45''8776'_490 ::
  T_IsDistributiveLattice_430 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_490 :: T_IsDistributiveLattice_430
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_490 T_IsDistributiveLattice_430
v0
  = let v1 :: T_IsLattice_348
v1 = T_IsDistributiveLattice_430 -> T_IsLattice_348
d_isLattice_440 (T_IsDistributiveLattice_430 -> T_IsDistributiveLattice_430
forall a b. a -> b
coe T_IsDistributiveLattice_430
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'737''45''8776'_106
            ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
               (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v2))))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.Eq.isPartialEquivalence
d_isPartialEquivalence_494 ::
  MAlonzo.Code.Agda.Primitive.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_430 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_494 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_430
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_494 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsDistributiveLattice_430
v8
  = T_IsDistributiveLattice_430 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_494 T_IsDistributiveLattice_430
v8
du_isPartialEquivalence_494 ::
  T_IsDistributiveLattice_430 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_494 :: T_IsDistributiveLattice_430 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_494 T_IsDistributiveLattice_430
v0
  = let v1 :: T_IsLattice_348
v1 = T_IsDistributiveLattice_430 -> T_IsLattice_348
d_isLattice_440 (T_IsDistributiveLattice_430 -> T_IsDistributiveLattice_430
forall a b. a -> b
coe T_IsDistributiveLattice_430
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreorder_76
v3
                = T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                    (T_IsPartialOrder_248 -> T_IsPartialOrder_248
forall a b. a -> b
coe T_IsPartialOrder_248
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
                  (T_IsPreorder_76 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_76
v3)))))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.Eq.refl
d_refl_496 :: T_IsDistributiveLattice_430 -> AgdaAny -> AgdaAny
d_refl_496 :: T_IsDistributiveLattice_430 -> AgdaAny -> AgdaAny
d_refl_496 T_IsDistributiveLattice_430
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 ((T_IsDistributiveLattice_430 -> T_IsLattice_348)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_430 -> T_IsLattice_348
d_isLattice_440 (T_IsDistributiveLattice_430 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_430
v0)))))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.Eq.reflexive
d_reflexive_498 ::
  MAlonzo.Code.Agda.Primitive.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_430 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_498 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_430
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_498 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 T_IsDistributiveLattice_430
v8
  = T_IsDistributiveLattice_430
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_498 T_IsDistributiveLattice_430
v8
du_reflexive_498 ::
  T_IsDistributiveLattice_430 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_498 :: T_IsDistributiveLattice_430
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_498 T_IsDistributiveLattice_430
v0
  = let v1 :: T_IsLattice_348
v1 = T_IsDistributiveLattice_430 -> T_IsLattice_348
d_isLattice_440 (T_IsDistributiveLattice_430 -> T_IsDistributiveLattice_430
forall a b. a -> b
coe T_IsDistributiveLattice_430
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreorder_76
v3
                = T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                    (T_IsPartialOrder_248 -> T_IsPartialOrder_248
forall a b. a -> b
coe T_IsPartialOrder_248
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
                    (T_IsPreorder_76 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_76
v3))
                 AgdaAny
v4)))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.Eq.sym
d_sym_500 ::
  T_IsDistributiveLattice_430 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_500 :: T_IsDistributiveLattice_430
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_500 T_IsDistributiveLattice_430
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 ((T_IsDistributiveLattice_430 -> T_IsLattice_348)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_430 -> T_IsLattice_348
d_isLattice_440 (T_IsDistributiveLattice_430 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_430
v0)))))
-- Relation.Binary.Lattice.Structures.IsDistributiveLattice._.Eq.trans
d_trans_502 ::
  T_IsDistributiveLattice_430 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_502 :: T_IsDistributiveLattice_430
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_502 T_IsDistributiveLattice_430
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 ((T_IsDistributiveLattice_430 -> T_IsLattice_348)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_430 -> T_IsLattice_348
d_isLattice_440 (T_IsDistributiveLattice_430 -> AgdaAny
forall a b. a -> b
coe T_IsDistributiveLattice_430
v0)))))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice
d_IsBoundedLattice_514 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsBoundedLattice_514 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 p
a8 p
a9 = ()
data T_IsBoundedLattice_514
  = C_constructor_600 T_IsLattice_348 (AgdaAny -> AgdaAny)
                      (AgdaAny -> AgdaAny)
-- Relation.Binary.Lattice.Structures.IsBoundedLattice.isLattice
d_isLattice_530 :: T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 :: T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 T_IsBoundedLattice_514
v0
  = case T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
v0 of
      C_constructor_600 T_IsLattice_348
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 -> T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v1
      T_IsBoundedLattice_514
_ -> T_IsLattice_348
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.Structures.IsBoundedLattice.maximum
d_maximum_532 :: T_IsBoundedLattice_514 -> AgdaAny -> AgdaAny
d_maximum_532 :: T_IsBoundedLattice_514 -> AgdaAny -> AgdaAny
d_maximum_532 T_IsBoundedLattice_514
v0
  = case T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
v0 of
      C_constructor_600 T_IsLattice_348
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v2
      T_IsBoundedLattice_514
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.Structures.IsBoundedLattice.minimum
d_minimum_534 :: T_IsBoundedLattice_514 -> AgdaAny -> AgdaAny
d_minimum_534 :: T_IsBoundedLattice_514 -> AgdaAny -> AgdaAny
d_minimum_534 T_IsBoundedLattice_514
v0
  = case T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
v0 of
      C_constructor_600 T_IsLattice_348
v1 AgdaAny -> AgdaAny
v2 AgdaAny -> AgdaAny
v3 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny
v3
      T_IsBoundedLattice_514
_ -> AgdaAny -> AgdaAny
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.antisym
d_antisym_538 ::
  T_IsBoundedLattice_514 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_538 :: T_IsBoundedLattice_514
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_538 T_IsBoundedLattice_514
v0
  = (T_IsPartialOrder_248
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_248
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_258
      ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514
v0)))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.infimum
d_infimum_540 ::
  T_IsBoundedLattice_514 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_infimum_540 :: T_IsBoundedLattice_514 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_540 T_IsBoundedLattice_514
v0 = (T_IsLattice_348 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsLattice_348 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_364 ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514
v0))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.isEquivalence
d_isEquivalence_542 ::
  T_IsBoundedLattice_514 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_542 :: T_IsBoundedLattice_514 -> T_IsEquivalence_28
d_isEquivalence_542 T_IsBoundedLattice_514
v0
  = (T_IsPreorder_76 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514
v0))))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.isJoinSemilattice
d_isJoinSemilattice_544 ::
  MAlonzo.Code.Agda.Primitive.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_514 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_544 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_514
-> T_IsJoinSemilattice_22
d_isJoinSemilattice_544 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny
v8 ~AgdaAny
v9 T_IsBoundedLattice_514
v10
  = T_IsBoundedLattice_514 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_544 T_IsBoundedLattice_514
v10
du_isJoinSemilattice_544 ::
  T_IsBoundedLattice_514 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_544 :: T_IsBoundedLattice_514 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_544 T_IsBoundedLattice_514
v0
  = (T_IsLattice_348 -> T_IsJoinSemilattice_22)
-> AgdaAny -> T_IsJoinSemilattice_22
forall a b. a -> b
coe T_IsLattice_348 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_366 ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514
v0))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.isMeetSemilattice
d_isMeetSemilattice_546 ::
  MAlonzo.Code.Agda.Primitive.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_514 -> T_IsMeetSemilattice_184
d_isMeetSemilattice_546 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_514
-> T_IsMeetSemilattice_184
d_isMeetSemilattice_546 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny
v8 ~AgdaAny
v9 T_IsBoundedLattice_514
v10
  = T_IsBoundedLattice_514 -> T_IsMeetSemilattice_184
du_isMeetSemilattice_546 T_IsBoundedLattice_514
v10
du_isMeetSemilattice_546 ::
  T_IsBoundedLattice_514 -> T_IsMeetSemilattice_184
du_isMeetSemilattice_546 :: T_IsBoundedLattice_514 -> T_IsMeetSemilattice_184
du_isMeetSemilattice_546 T_IsBoundedLattice_514
v0
  = (T_IsLattice_348 -> T_IsMeetSemilattice_184)
-> AgdaAny -> T_IsMeetSemilattice_184
forall a b. a -> b
coe T_IsLattice_348 -> T_IsMeetSemilattice_184
du_isMeetSemilattice_368 ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514
v0))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.isPartialOrder
d_isPartialOrder_548 ::
  T_IsBoundedLattice_514 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_248
d_isPartialOrder_548 :: T_IsBoundedLattice_514 -> T_IsPartialOrder_248
d_isPartialOrder_548 T_IsBoundedLattice_514
v0
  = (T_IsLattice_348 -> T_IsPartialOrder_248)
-> AgdaAny -> T_IsPartialOrder_248
forall a b. a -> b
coe T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514
v0))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.isPreorder
d_isPreorder_550 ::
  T_IsBoundedLattice_514 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_76
d_isPreorder_550 :: T_IsBoundedLattice_514 -> T_IsPreorder_76
d_isPreorder_550 T_IsBoundedLattice_514
v0
  = (T_IsPartialOrder_248 -> T_IsPreorder_76)
-> AgdaAny -> T_IsPreorder_76
forall a b. a -> b
coe
      T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
      ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514
v0)))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.refl
d_refl_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_514 -> AgdaAny -> AgdaAny
d_refl_552 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_514
-> AgdaAny
-> AgdaAny
d_refl_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_514
v10
  = T_IsBoundedLattice_514 -> AgdaAny -> AgdaAny
du_refl_552 T_IsBoundedLattice_514
v10
du_refl_552 :: T_IsBoundedLattice_514 -> AgdaAny -> AgdaAny
du_refl_552 :: T_IsBoundedLattice_514 -> AgdaAny -> AgdaAny
du_refl_552 T_IsBoundedLattice_514
v0
  = let v1 :: T_IsLattice_348
v1 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_76 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_76 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_104
            ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
               (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.reflexive
d_reflexive_554 ::
  T_IsBoundedLattice_514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_554 :: T_IsBoundedLattice_514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_554 T_IsBoundedLattice_514
v0
  = (T_IsPreorder_76 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_76 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_88
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514
v0))))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.supremum
d_supremum_556 ::
  T_IsBoundedLattice_514 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_supremum_556 :: T_IsBoundedLattice_514 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_556 T_IsBoundedLattice_514
v0
  = (T_IsLattice_348 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsLattice_348 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_362 ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514
v0))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.trans
d_trans_558 ::
  T_IsBoundedLattice_514 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_558 :: T_IsBoundedLattice_514
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_558 T_IsBoundedLattice_514
v0
  = (T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_90
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514
v0))))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.x∧y≤x
d_x'8743'y'8804'x_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_514 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'x_560 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_514
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'x_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_514
v10
  = T_IsBoundedLattice_514 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_560 T_IsBoundedLattice_514
v10
du_x'8743'y'8804'x_560 ::
  T_IsBoundedLattice_514 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_560 :: T_IsBoundedLattice_514 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_560 T_IsBoundedLattice_514
v0
  = let v1 :: T_IsLattice_348
v1 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_200 ((T_IsLattice_348 -> T_IsMeetSemilattice_184) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsMeetSemilattice_184
du_isMeetSemilattice_368 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v1)))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.x∧y≤y
d_x'8743'y'8804'y_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_514 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'y_562 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_514
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'y_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_514
v10
  = T_IsBoundedLattice_514 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_562 T_IsBoundedLattice_514
v10
du_x'8743'y'8804'y_562 ::
  T_IsBoundedLattice_514 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_562 :: T_IsBoundedLattice_514 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_562 T_IsBoundedLattice_514
v0
  = let v1 :: T_IsLattice_348
v1 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_212 ((T_IsLattice_348 -> T_IsMeetSemilattice_184) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsMeetSemilattice_184
du_isMeetSemilattice_368 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v1)))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.x≤x∨y
d_x'8804'x'8744'y_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_514 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8804'x'8744'y_564 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_514
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8804'x'8744'y_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_514
v10
  = T_IsBoundedLattice_514 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_564 T_IsBoundedLattice_514
v10
du_x'8804'x'8744'y_564 ::
  T_IsBoundedLattice_514 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_564 :: T_IsBoundedLattice_514 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_564 T_IsBoundedLattice_514
v0
  = let v1 :: T_IsLattice_348
v1 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
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_348 -> T_IsJoinSemilattice_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_366 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v1)))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.y≤x∨y
d_y'8804'x'8744'y_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_514 -> AgdaAny -> AgdaAny -> AgdaAny
d_y'8804'x'8744'y_566 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_514
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_y'8804'x'8744'y_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_514
v10
  = T_IsBoundedLattice_514 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_566 T_IsBoundedLattice_514
v10
du_y'8804'x'8744'y_566 ::
  T_IsBoundedLattice_514 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_566 :: T_IsBoundedLattice_514 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_566 T_IsBoundedLattice_514
v0
  = let v1 :: T_IsLattice_348
v1 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
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_348 -> T_IsJoinSemilattice_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_366 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v1)))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.∧-greatest
d_'8743''45'greatest_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_514 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'greatest_568 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_514
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'greatest_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_514
v10
  = T_IsBoundedLattice_514
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_568 T_IsBoundedLattice_514
v10
du_'8743''45'greatest_568 ::
  T_IsBoundedLattice_514 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_568 :: T_IsBoundedLattice_514
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_568 T_IsBoundedLattice_514
v0
  = let v1 :: T_IsLattice_348
v1 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_IsMeetSemilattice_184
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsMeetSemilattice_184
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_226 ((T_IsLattice_348 -> T_IsMeetSemilattice_184) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsMeetSemilattice_184
du_isMeetSemilattice_368 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v1)))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.∨-least
d_'8744''45'least_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_514 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'least_570 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_514
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'least_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_514
v10
  = T_IsBoundedLattice_514
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_570 T_IsBoundedLattice_514
v10
du_'8744''45'least_570 ::
  T_IsBoundedLattice_514 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_570 :: T_IsBoundedLattice_514
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_570 T_IsBoundedLattice_514
v0
  = let v1 :: T_IsLattice_348
v1 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
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_348 -> T_IsJoinSemilattice_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_366 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v1)))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.∼-resp-≈
d_'8764''45'resp'45''8776'_572 ::
  MAlonzo.Code.Agda.Primitive.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_514 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_572 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_514
-> T_Σ_14
d_'8764''45'resp'45''8776'_572 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny
v8
                               ~AgdaAny
v9 T_IsBoundedLattice_514
v10
  = T_IsBoundedLattice_514 -> T_Σ_14
du_'8764''45'resp'45''8776'_572 T_IsBoundedLattice_514
v10
du_'8764''45'resp'45''8776'_572 ::
  T_IsBoundedLattice_514 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_572 :: T_IsBoundedLattice_514 -> T_Σ_14
du_'8764''45'resp'45''8776'_572 T_IsBoundedLattice_514
v0
  = let v1 :: T_IsLattice_348
v1 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_76 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_76 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_124
            ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
               (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_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_514 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_574 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_514
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_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_514
v10
  = T_IsBoundedLattice_514
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_574 T_IsBoundedLattice_514
v10
du_'8764''45'resp'691''45''8776'_574 ::
  T_IsBoundedLattice_514 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_574 :: T_IsBoundedLattice_514
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_574 T_IsBoundedLattice_514
v0
  = let v1 :: T_IsLattice_348
v1 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_122
            ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
               (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_576 ::
  MAlonzo.Code.Agda.Primitive.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_514 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_576 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_514
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_576 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7
                                    ~AgdaAny
v8 ~AgdaAny
v9 T_IsBoundedLattice_514
v10
  = T_IsBoundedLattice_514
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_576 T_IsBoundedLattice_514
v10
du_'8764''45'resp'737''45''8776'_576 ::
  T_IsBoundedLattice_514 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_576 :: T_IsBoundedLattice_514
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_576 T_IsBoundedLattice_514
v0
  = let v1 :: T_IsLattice_348
v1 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_120
            ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
               (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.≲-resp-≈
d_'8818''45'resp'45''8776'_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_514 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8818''45'resp'45''8776'_578 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_514
-> T_Σ_14
d_'8818''45'resp'45''8776'_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_514
v10
  = T_IsBoundedLattice_514 -> T_Σ_14
du_'8818''45'resp'45''8776'_578 T_IsBoundedLattice_514
v10
du_'8818''45'resp'45''8776'_578 ::
  T_IsBoundedLattice_514 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8818''45'resp'45''8776'_578 :: T_IsBoundedLattice_514 -> T_Σ_14
du_'8818''45'resp'45''8776'_578 T_IsBoundedLattice_514
v0
  = let v1 :: T_IsLattice_348
v1 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_76 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_76 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'45''8776'_118
            ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
               (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.≲-respʳ-≈
d_'8818''45'resp'691''45''8776'_580 ::
  MAlonzo.Code.Agda.Primitive.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_514 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'691''45''8776'_580 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_514
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'691''45''8776'_580 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7
                                    ~AgdaAny
v8 ~AgdaAny
v9 T_IsBoundedLattice_514
v10
  = T_IsBoundedLattice_514
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_580 T_IsBoundedLattice_514
v10
du_'8818''45'resp'691''45''8776'_580 ::
  T_IsBoundedLattice_514 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_580 :: T_IsBoundedLattice_514
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_580 T_IsBoundedLattice_514
v0
  = let v1 :: T_IsLattice_348
v1 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'691''45''8776'_112
            ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
               (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.≲-respˡ-≈
d_'8818''45'resp'737''45''8776'_582 ::
  MAlonzo.Code.Agda.Primitive.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_514 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'737''45''8776'_582 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_514
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'737''45''8776'_582 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7
                                    ~AgdaAny
v8 ~AgdaAny
v9 T_IsBoundedLattice_514
v10
  = T_IsBoundedLattice_514
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_582 T_IsBoundedLattice_514
v10
du_'8818''45'resp'737''45''8776'_582 ::
  T_IsBoundedLattice_514 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_582 :: T_IsBoundedLattice_514
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_582 T_IsBoundedLattice_514
v0
  = let v1 :: T_IsLattice_348
v1 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'737''45''8776'_106
            ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
               (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v2))))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.Eq.isPartialEquivalence
d_isPartialEquivalence_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_514 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_586 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_514
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_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_514
v10
  = T_IsBoundedLattice_514 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_586 T_IsBoundedLattice_514
v10
du_isPartialEquivalence_586 ::
  T_IsBoundedLattice_514 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_586 :: T_IsBoundedLattice_514 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_586 T_IsBoundedLattice_514
v0
  = let v1 :: T_IsLattice_348
v1 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreorder_76
v3
                = T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                    (T_IsPartialOrder_248 -> T_IsPartialOrder_248
forall a b. a -> b
coe T_IsPartialOrder_248
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
               ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
                  (T_IsPreorder_76 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_76
v3)))))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.Eq.refl
d_refl_588 :: T_IsBoundedLattice_514 -> AgdaAny -> AgdaAny
d_refl_588 :: T_IsBoundedLattice_514 -> AgdaAny -> AgdaAny
d_refl_588 T_IsBoundedLattice_514
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514
v0)))))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.Eq.reflexive
d_reflexive_590 ::
  MAlonzo.Code.Agda.Primitive.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_514 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_590 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_514
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_590 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny
v8 ~AgdaAny
v9 T_IsBoundedLattice_514
v10
  = T_IsBoundedLattice_514
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_590 T_IsBoundedLattice_514
v10
du_reflexive_590 ::
  T_IsBoundedLattice_514 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_590 :: T_IsBoundedLattice_514
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_590 T_IsBoundedLattice_514
v0
  = let v1 :: T_IsLattice_348
v1 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsPartialOrder_248
v2 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPreorder_76
v3
                = T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                    (T_IsPartialOrder_248 -> T_IsPartialOrder_248
forall a b. a -> b
coe T_IsPartialOrder_248
v2) in
          (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
            (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
               (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                 ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
                    (T_IsPreorder_76 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_76
v3))
                 AgdaAny
v4)))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.Eq.sym
d_sym_592 ::
  T_IsBoundedLattice_514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_592 :: T_IsBoundedLattice_514 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_592 T_IsBoundedLattice_514
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514
v0)))))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice._.Eq.trans
d_trans_594 ::
  T_IsBoundedLattice_514 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_594 :: T_IsBoundedLattice_514
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_594 T_IsBoundedLattice_514
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514
v0)))))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice.isBoundedJoinSemilattice
d_isBoundedJoinSemilattice_596 ::
  MAlonzo.Code.Agda.Primitive.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_514 -> T_IsBoundedJoinSemilattice_118
d_isBoundedJoinSemilattice_596 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_514
-> T_IsBoundedJoinSemilattice_118
d_isBoundedJoinSemilattice_596 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny
v8
                               ~AgdaAny
v9 T_IsBoundedLattice_514
v10
  = T_IsBoundedLattice_514 -> T_IsBoundedJoinSemilattice_118
du_isBoundedJoinSemilattice_596 T_IsBoundedLattice_514
v10
du_isBoundedJoinSemilattice_596 ::
  T_IsBoundedLattice_514 -> T_IsBoundedJoinSemilattice_118
du_isBoundedJoinSemilattice_596 :: T_IsBoundedLattice_514 -> T_IsBoundedJoinSemilattice_118
du_isBoundedJoinSemilattice_596 T_IsBoundedLattice_514
v0
  = (T_IsJoinSemilattice_22
 -> (AgdaAny -> AgdaAny) -> T_IsBoundedJoinSemilattice_118)
-> AgdaAny -> AgdaAny -> T_IsBoundedJoinSemilattice_118
forall a b. a -> b
coe
      T_IsJoinSemilattice_22
-> (AgdaAny -> AgdaAny) -> T_IsBoundedJoinSemilattice_118
C_constructor_180
      ((T_IsLattice_348 -> T_IsJoinSemilattice_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_366 ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514
v0)))
      ((T_IsBoundedLattice_514 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514 -> AgdaAny -> AgdaAny
d_minimum_534 (T_IsBoundedLattice_514 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514
v0))
-- Relation.Binary.Lattice.Structures.IsBoundedLattice.isBoundedMeetSemilattice
d_isBoundedMeetSemilattice_598 ::
  MAlonzo.Code.Agda.Primitive.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_514 -> T_IsBoundedMeetSemilattice_280
d_isBoundedMeetSemilattice_598 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBoundedLattice_514
-> T_IsBoundedMeetSemilattice_280
d_isBoundedMeetSemilattice_598 ~()
v0 ~()
v1 ~()
v2 ~()
v3 ~AgdaAny -> AgdaAny -> ()
v4 ~AgdaAny -> AgdaAny -> ()
v5 ~AgdaAny -> AgdaAny -> AgdaAny
v6 ~AgdaAny -> AgdaAny -> AgdaAny
v7 ~AgdaAny
v8
                               ~AgdaAny
v9 T_IsBoundedLattice_514
v10
  = T_IsBoundedLattice_514 -> T_IsBoundedMeetSemilattice_280
du_isBoundedMeetSemilattice_598 T_IsBoundedLattice_514
v10
du_isBoundedMeetSemilattice_598 ::
  T_IsBoundedLattice_514 -> T_IsBoundedMeetSemilattice_280
du_isBoundedMeetSemilattice_598 :: T_IsBoundedLattice_514 -> T_IsBoundedMeetSemilattice_280
du_isBoundedMeetSemilattice_598 T_IsBoundedLattice_514
v0
  = (T_IsMeetSemilattice_184
 -> (AgdaAny -> AgdaAny) -> T_IsBoundedMeetSemilattice_280)
-> AgdaAny -> AgdaAny -> T_IsBoundedMeetSemilattice_280
forall a b. a -> b
coe
      T_IsMeetSemilattice_184
-> (AgdaAny -> AgdaAny) -> T_IsBoundedMeetSemilattice_280
C_constructor_342
      ((T_IsLattice_348 -> T_IsMeetSemilattice_184) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsMeetSemilattice_184
du_isMeetSemilattice_368 ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514
v0)))
      ((T_IsBoundedLattice_514 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514 -> AgdaAny -> AgdaAny
d_maximum_532 (T_IsBoundedLattice_514 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514
v0))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra
d_IsHeytingAlgebra_612 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsHeytingAlgebra_612 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_612
  = C_constructor_734 T_IsBoundedLattice_514
                      (AgdaAny ->
                       AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14)
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra.isBoundedLattice
d_isBoundedLattice_628 ::
  T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 :: T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 T_IsHeytingAlgebra_612
v0
  = case T_IsHeytingAlgebra_612 -> T_IsHeytingAlgebra_612
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v0 of
      C_constructor_734 T_IsBoundedLattice_514
v1 AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
v2 -> T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
v1
      T_IsHeytingAlgebra_612
_ -> T_IsBoundedLattice_514
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra.exponential
d_exponential_630 ::
  T_IsHeytingAlgebra_612 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_exponential_630 :: T_IsHeytingAlgebra_612 -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
d_exponential_630 T_IsHeytingAlgebra_612
v0
  = case T_IsHeytingAlgebra_612 -> T_IsHeytingAlgebra_612
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v0 of
      C_constructor_734 T_IsBoundedLattice_514
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_612
_ -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra.transpose-⇨
d_transpose'45''8680'_638 ::
  MAlonzo.Code.Agda.Primitive.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_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_transpose'45''8680'_638 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_transpose'45''8680'_638 ~()
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_612
v11 AgdaAny
v12 AgdaAny
v13 AgdaAny
v14
  = T_IsHeytingAlgebra_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8680'_638 T_IsHeytingAlgebra_612
v11 AgdaAny
v12 AgdaAny
v13 AgdaAny
v14
du_transpose'45''8680'_638 ::
  T_IsHeytingAlgebra_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8680'_638 :: T_IsHeytingAlgebra_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8680'_638 T_IsHeytingAlgebra_612
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_612 -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14)
-> T_IsHeytingAlgebra_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612 -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
d_exponential_630 T_IsHeytingAlgebra_612
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3)
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra.transpose-∧
d_transpose'45''8743'_654 ::
  MAlonzo.Code.Agda.Primitive.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_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_transpose'45''8743'_654 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_transpose'45''8743'_654 ~()
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_612
v11 AgdaAny
v12 AgdaAny
v13 AgdaAny
v14
  = T_IsHeytingAlgebra_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8743'_654 T_IsHeytingAlgebra_612
v11 AgdaAny
v12 AgdaAny
v13 AgdaAny
v14
du_transpose'45''8743'_654 ::
  T_IsHeytingAlgebra_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8743'_654 :: T_IsHeytingAlgebra_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8743'_654 T_IsHeytingAlgebra_612
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_612 -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14)
-> T_IsHeytingAlgebra_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612 -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
d_exponential_630 T_IsHeytingAlgebra_612
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3)
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.antisym
d_antisym_666 ::
  T_IsHeytingAlgebra_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_666 :: T_IsHeytingAlgebra_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_666 T_IsHeytingAlgebra_612
v0
  = (T_IsPartialOrder_248
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_248
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_258
      ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360
         ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 ((T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v0))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.infimum
d_infimum_668 ::
  T_IsHeytingAlgebra_612 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_infimum_668 :: T_IsHeytingAlgebra_612 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_668 T_IsHeytingAlgebra_612
v0
  = (T_IsLattice_348 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsLattice_348 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_364
      ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 ((T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v0)))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.isBoundedJoinSemilattice
d_isBoundedJoinSemilattice_670 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsHeytingAlgebra_612 -> T_IsBoundedJoinSemilattice_118
d_isBoundedJoinSemilattice_670 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_612
-> T_IsBoundedJoinSemilattice_118
d_isBoundedJoinSemilattice_670 ~()
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_612
v11
  = T_IsHeytingAlgebra_612 -> T_IsBoundedJoinSemilattice_118
du_isBoundedJoinSemilattice_670 T_IsHeytingAlgebra_612
v11
du_isBoundedJoinSemilattice_670 ::
  T_IsHeytingAlgebra_612 -> T_IsBoundedJoinSemilattice_118
du_isBoundedJoinSemilattice_670 :: T_IsHeytingAlgebra_612 -> T_IsBoundedJoinSemilattice_118
du_isBoundedJoinSemilattice_670 T_IsHeytingAlgebra_612
v0
  = (T_IsBoundedLattice_514 -> T_IsBoundedJoinSemilattice_118)
-> AgdaAny -> T_IsBoundedJoinSemilattice_118
forall a b. a -> b
coe
      T_IsBoundedLattice_514 -> T_IsBoundedJoinSemilattice_118
du_isBoundedJoinSemilattice_596
      ((T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v0))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.isBoundedMeetSemilattice
d_isBoundedMeetSemilattice_672 ::
  MAlonzo.Code.Agda.Primitive.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_612 -> T_IsBoundedMeetSemilattice_280
d_isBoundedMeetSemilattice_672 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_612
-> T_IsBoundedMeetSemilattice_280
d_isBoundedMeetSemilattice_672 ~()
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_612
v11
  = T_IsHeytingAlgebra_612 -> T_IsBoundedMeetSemilattice_280
du_isBoundedMeetSemilattice_672 T_IsHeytingAlgebra_612
v11
du_isBoundedMeetSemilattice_672 ::
  T_IsHeytingAlgebra_612 -> T_IsBoundedMeetSemilattice_280
du_isBoundedMeetSemilattice_672 :: T_IsHeytingAlgebra_612 -> T_IsBoundedMeetSemilattice_280
du_isBoundedMeetSemilattice_672 T_IsHeytingAlgebra_612
v0
  = (T_IsBoundedLattice_514 -> T_IsBoundedMeetSemilattice_280)
-> AgdaAny -> T_IsBoundedMeetSemilattice_280
forall a b. a -> b
coe
      T_IsBoundedLattice_514 -> T_IsBoundedMeetSemilattice_280
du_isBoundedMeetSemilattice_598
      ((T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v0))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.isEquivalence
d_isEquivalence_674 ::
  T_IsHeytingAlgebra_612 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_674 :: T_IsHeytingAlgebra_612 -> T_IsEquivalence_28
d_isEquivalence_674 T_IsHeytingAlgebra_612
v0
  = (T_IsPreorder_76 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360
            ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 ((T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v0)))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.isJoinSemilattice
d_isJoinSemilattice_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_612 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_676 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_612
-> T_IsJoinSemilattice_22
d_isJoinSemilattice_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_612
v11
  = T_IsHeytingAlgebra_612 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_676 T_IsHeytingAlgebra_612
v11
du_isJoinSemilattice_676 ::
  T_IsHeytingAlgebra_612 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_676 :: T_IsHeytingAlgebra_612 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_676 T_IsHeytingAlgebra_612
v0
  = let v1 :: T_IsBoundedLattice_514
v1 = T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> T_IsHeytingAlgebra_612
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v0) in
    AgdaAny -> T_IsJoinSemilattice_22
forall a b. a -> b
coe ((T_IsLattice_348 -> T_IsJoinSemilattice_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_366 ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514
v1)))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.isLattice
d_isLattice_678 :: T_IsHeytingAlgebra_612 -> T_IsLattice_348
d_isLattice_678 :: T_IsHeytingAlgebra_612 -> T_IsLattice_348
d_isLattice_678 T_IsHeytingAlgebra_612
v0
  = (T_IsBoundedLattice_514 -> T_IsLattice_348)
-> AgdaAny -> T_IsLattice_348
forall a b. a -> b
coe T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 ((T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v0))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.isMeetSemilattice
d_isMeetSemilattice_680 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> T_IsHeytingAlgebra_612 -> T_IsMeetSemilattice_184
d_isMeetSemilattice_680 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_612
-> T_IsMeetSemilattice_184
d_isMeetSemilattice_680 ~()
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_612
v11
  = T_IsHeytingAlgebra_612 -> T_IsMeetSemilattice_184
du_isMeetSemilattice_680 T_IsHeytingAlgebra_612
v11
du_isMeetSemilattice_680 ::
  T_IsHeytingAlgebra_612 -> T_IsMeetSemilattice_184
du_isMeetSemilattice_680 :: T_IsHeytingAlgebra_612 -> T_IsMeetSemilattice_184
du_isMeetSemilattice_680 T_IsHeytingAlgebra_612
v0
  = let v1 :: T_IsBoundedLattice_514
v1 = T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> T_IsHeytingAlgebra_612
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v0) in
    AgdaAny -> T_IsMeetSemilattice_184
forall a b. a -> b
coe ((T_IsLattice_348 -> T_IsMeetSemilattice_184) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsMeetSemilattice_184
du_isMeetSemilattice_368 ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514
v1)))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.isPartialOrder
d_isPartialOrder_682 ::
  T_IsHeytingAlgebra_612 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_248
d_isPartialOrder_682 :: T_IsHeytingAlgebra_612 -> T_IsPartialOrder_248
d_isPartialOrder_682 T_IsHeytingAlgebra_612
v0
  = (T_IsLattice_348 -> T_IsPartialOrder_248)
-> AgdaAny -> T_IsPartialOrder_248
forall a b. a -> b
coe
      T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360
      ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 ((T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v0)))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.isPreorder
d_isPreorder_684 ::
  T_IsHeytingAlgebra_612 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_76
d_isPreorder_684 :: T_IsHeytingAlgebra_612 -> T_IsPreorder_76
d_isPreorder_684 T_IsHeytingAlgebra_612
v0
  = (T_IsPartialOrder_248 -> T_IsPreorder_76)
-> AgdaAny -> T_IsPreorder_76
forall a b. a -> b
coe
      T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
      ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360
         ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 ((T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v0))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.maximum
d_maximum_686 :: T_IsHeytingAlgebra_612 -> AgdaAny -> AgdaAny
d_maximum_686 :: T_IsHeytingAlgebra_612 -> AgdaAny -> AgdaAny
d_maximum_686 T_IsHeytingAlgebra_612
v0
  = (T_IsBoundedLattice_514 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514 -> AgdaAny -> AgdaAny
d_maximum_532 ((T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v0))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.minimum
d_minimum_688 :: T_IsHeytingAlgebra_612 -> AgdaAny -> AgdaAny
d_minimum_688 :: T_IsHeytingAlgebra_612 -> AgdaAny -> AgdaAny
d_minimum_688 T_IsHeytingAlgebra_612
v0
  = (T_IsBoundedLattice_514 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514 -> AgdaAny -> AgdaAny
d_minimum_534 ((T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v0))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.refl
d_refl_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_612 -> AgdaAny -> AgdaAny
d_refl_690 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_612
-> AgdaAny
-> AgdaAny
d_refl_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_612
v11
  = T_IsHeytingAlgebra_612 -> AgdaAny -> AgdaAny
du_refl_690 T_IsHeytingAlgebra_612
v11
du_refl_690 :: T_IsHeytingAlgebra_612 -> AgdaAny -> AgdaAny
du_refl_690 :: T_IsHeytingAlgebra_612 -> AgdaAny -> AgdaAny
du_refl_690 T_IsHeytingAlgebra_612
v0
  = let v1 :: T_IsBoundedLattice_514
v1 = T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> T_IsHeytingAlgebra_612
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_348
v2 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_248
v3 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsPreorder_76 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_76 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_104
               ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                  (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v3)))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.reflexive
d_reflexive_692 ::
  T_IsHeytingAlgebra_612 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_692 :: T_IsHeytingAlgebra_612 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_692 T_IsHeytingAlgebra_612
v0
  = (T_IsPreorder_76 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_76 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_88
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360
            ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 ((T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v0)))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.supremum
d_supremum_694 ::
  T_IsHeytingAlgebra_612 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_supremum_694 :: T_IsHeytingAlgebra_612 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_694 T_IsHeytingAlgebra_612
v0
  = (T_IsLattice_348 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsLattice_348 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_362
      ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 ((T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v0)))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.trans
d_trans_696 ::
  T_IsHeytingAlgebra_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_696 :: T_IsHeytingAlgebra_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_696 T_IsHeytingAlgebra_612
v0
  = (T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_90
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360
            ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 ((T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v0)))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.x∧y≤x
d_x'8743'y'8804'x_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_612 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'x_698 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'x_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_612
v11
  = T_IsHeytingAlgebra_612 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_698 T_IsHeytingAlgebra_612
v11
du_x'8743'y'8804'x_698 ::
  T_IsHeytingAlgebra_612 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_698 :: T_IsHeytingAlgebra_612 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_698 T_IsHeytingAlgebra_612
v0
  = let v1 :: T_IsBoundedLattice_514
v1 = T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> T_IsHeytingAlgebra_612
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_348
v2 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_200 ((T_IsLattice_348 -> T_IsMeetSemilattice_184) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsMeetSemilattice_184
du_isMeetSemilattice_368 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v2))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.x∧y≤y
d_x'8743'y'8804'y_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_612 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'y_700 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'y_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_612
v11
  = T_IsHeytingAlgebra_612 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_700 T_IsHeytingAlgebra_612
v11
du_x'8743'y'8804'y_700 ::
  T_IsHeytingAlgebra_612 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_700 :: T_IsHeytingAlgebra_612 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_700 T_IsHeytingAlgebra_612
v0
  = let v1 :: T_IsBoundedLattice_514
v1 = T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> T_IsHeytingAlgebra_612
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_348
v2 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_212 ((T_IsLattice_348 -> T_IsMeetSemilattice_184) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsMeetSemilattice_184
du_isMeetSemilattice_368 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v2))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.x≤x∨y
d_x'8804'x'8744'y_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_612 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8804'x'8744'y_702 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8804'x'8744'y_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_612
v11
  = T_IsHeytingAlgebra_612 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_702 T_IsHeytingAlgebra_612
v11
du_x'8804'x'8744'y_702 ::
  T_IsHeytingAlgebra_612 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_702 :: T_IsHeytingAlgebra_612 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_702 T_IsHeytingAlgebra_612
v0
  = let v1 :: T_IsBoundedLattice_514
v1 = T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> T_IsHeytingAlgebra_612
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_348
v2 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
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_348 -> T_IsJoinSemilattice_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_366 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v2))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.y≤x∨y
d_y'8804'x'8744'y_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_612 -> AgdaAny -> AgdaAny -> AgdaAny
d_y'8804'x'8744'y_704 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_y'8804'x'8744'y_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_612
v11
  = T_IsHeytingAlgebra_612 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_704 T_IsHeytingAlgebra_612
v11
du_y'8804'x'8744'y_704 ::
  T_IsHeytingAlgebra_612 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_704 :: T_IsHeytingAlgebra_612 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_704 T_IsHeytingAlgebra_612
v0
  = let v1 :: T_IsBoundedLattice_514
v1 = T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> T_IsHeytingAlgebra_612
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_348
v2 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
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_348 -> T_IsJoinSemilattice_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_366 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v2))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.∧-greatest
d_'8743''45'greatest_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_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'greatest_706 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'greatest_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_612
v11
  = T_IsHeytingAlgebra_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_706 T_IsHeytingAlgebra_612
v11
du_'8743''45'greatest_706 ::
  T_IsHeytingAlgebra_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_706 :: T_IsHeytingAlgebra_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_706 T_IsHeytingAlgebra_612
v0
  = let v1 :: T_IsBoundedLattice_514
v1 = T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> T_IsHeytingAlgebra_612
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_348
v2 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_IsMeetSemilattice_184
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsMeetSemilattice_184
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_226 ((T_IsLattice_348 -> T_IsMeetSemilattice_184) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsMeetSemilattice_184
du_isMeetSemilattice_368 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v2))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.∨-least
d_'8744''45'least_708 ::
  MAlonzo.Code.Agda.Primitive.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_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'least_708 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'least_708 ~()
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_612
v11
  = T_IsHeytingAlgebra_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_708 T_IsHeytingAlgebra_612
v11
du_'8744''45'least_708 ::
  T_IsHeytingAlgebra_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_708 :: T_IsHeytingAlgebra_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_708 T_IsHeytingAlgebra_612
v0
  = let v1 :: T_IsBoundedLattice_514
v1 = T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> T_IsHeytingAlgebra_612
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_348
v2 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
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_348 -> T_IsJoinSemilattice_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_366 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v2))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.∼-resp-≈
d_'8764''45'resp'45''8776'_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_612 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_710 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_612
-> T_Σ_14
d_'8764''45'resp'45''8776'_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_612
v11
  = T_IsHeytingAlgebra_612 -> T_Σ_14
du_'8764''45'resp'45''8776'_710 T_IsHeytingAlgebra_612
v11
du_'8764''45'resp'45''8776'_710 ::
  T_IsHeytingAlgebra_612 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_710 :: T_IsHeytingAlgebra_612 -> T_Σ_14
du_'8764''45'resp'45''8776'_710 T_IsHeytingAlgebra_612
v0
  = let v1 :: T_IsBoundedLattice_514
v1 = T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> T_IsHeytingAlgebra_612
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_348
v2 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_248
v3 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsPreorder_76 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_76 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_124
               ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                  (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v3)))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_712 ::
  MAlonzo.Code.Agda.Primitive.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_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_712 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_712 ~()
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_612
v11
  = T_IsHeytingAlgebra_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_712 T_IsHeytingAlgebra_612
v11
du_'8764''45'resp'691''45''8776'_712 ::
  T_IsHeytingAlgebra_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_712 :: T_IsHeytingAlgebra_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_712 T_IsHeytingAlgebra_612
v0
  = let v1 :: T_IsBoundedLattice_514
v1 = T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> T_IsHeytingAlgebra_612
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_348
v2 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_248
v3 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_122
               ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                  (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v3)))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_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_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_714 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_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_612
v11
  = T_IsHeytingAlgebra_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_714 T_IsHeytingAlgebra_612
v11
du_'8764''45'resp'737''45''8776'_714 ::
  T_IsHeytingAlgebra_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_714 :: T_IsHeytingAlgebra_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_714 T_IsHeytingAlgebra_612
v0
  = let v1 :: T_IsBoundedLattice_514
v1 = T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> T_IsHeytingAlgebra_612
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_348
v2 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_248
v3 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_120
               ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                  (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v3)))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.≲-resp-≈
d_'8818''45'resp'45''8776'_716 ::
  MAlonzo.Code.Agda.Primitive.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_612 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8818''45'resp'45''8776'_716 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_612
-> T_Σ_14
d_'8818''45'resp'45''8776'_716 ~()
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_612
v11
  = T_IsHeytingAlgebra_612 -> T_Σ_14
du_'8818''45'resp'45''8776'_716 T_IsHeytingAlgebra_612
v11
du_'8818''45'resp'45''8776'_716 ::
  T_IsHeytingAlgebra_612 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8818''45'resp'45''8776'_716 :: T_IsHeytingAlgebra_612 -> T_Σ_14
du_'8818''45'resp'45''8776'_716 T_IsHeytingAlgebra_612
v0
  = let v1 :: T_IsBoundedLattice_514
v1 = T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> T_IsHeytingAlgebra_612
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_348
v2 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_248
v3 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsPreorder_76 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_76 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'45''8776'_118
               ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                  (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v3)))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.≲-respʳ-≈
d_'8818''45'resp'691''45''8776'_718 ::
  MAlonzo.Code.Agda.Primitive.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_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'691''45''8776'_718 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'691''45''8776'_718 ~()
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_612
v11
  = T_IsHeytingAlgebra_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_718 T_IsHeytingAlgebra_612
v11
du_'8818''45'resp'691''45''8776'_718 ::
  T_IsHeytingAlgebra_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_718 :: T_IsHeytingAlgebra_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_718 T_IsHeytingAlgebra_612
v0
  = let v1 :: T_IsBoundedLattice_514
v1 = T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> T_IsHeytingAlgebra_612
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_348
v2 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_248
v3 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'691''45''8776'_112
               ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                  (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v3)))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.≲-respˡ-≈
d_'8818''45'resp'737''45''8776'_720 ::
  MAlonzo.Code.Agda.Primitive.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_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'737''45''8776'_720 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_612
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'737''45''8776'_720 ~()
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_612
v11
  = T_IsHeytingAlgebra_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_720 T_IsHeytingAlgebra_612
v11
du_'8818''45'resp'737''45''8776'_720 ::
  T_IsHeytingAlgebra_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_720 :: T_IsHeytingAlgebra_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_720 T_IsHeytingAlgebra_612
v0
  = let v1 :: T_IsBoundedLattice_514
v1 = T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> T_IsHeytingAlgebra_612
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_348
v2 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_248
v3 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'737''45''8776'_106
               ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                  (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v3)))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.Eq.isPartialEquivalence
d_isPartialEquivalence_724 ::
  MAlonzo.Code.Agda.Primitive.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_612 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_724 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_612
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_724 ~()
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_612
v11
  = T_IsHeytingAlgebra_612 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_724 T_IsHeytingAlgebra_612
v11
du_isPartialEquivalence_724 ::
  T_IsHeytingAlgebra_612 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_724 :: T_IsHeytingAlgebra_612 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_724 T_IsHeytingAlgebra_612
v0
  = let v1 :: T_IsBoundedLattice_514
v1 = T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> T_IsHeytingAlgebra_612
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_348
v2 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_248
v3 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreorder_76
v4
                   = T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                       (T_IsPartialOrder_248 -> T_IsPartialOrder_248
forall a b. a -> b
coe T_IsPartialOrder_248
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                  ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
                     (T_IsPreorder_76 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_76
v4))))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.Eq.refl
d_refl_726 :: T_IsHeytingAlgebra_612 -> AgdaAny -> AgdaAny
d_refl_726 :: T_IsHeytingAlgebra_612 -> AgdaAny -> AgdaAny
d_refl_726 T_IsHeytingAlgebra_612
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360
               ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 ((T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v0))))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.Eq.reflexive
d_reflexive_728 ::
  MAlonzo.Code.Agda.Primitive.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_612 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_728 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsHeytingAlgebra_612
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_728 ~()
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_612
v11
  = T_IsHeytingAlgebra_612
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_728 T_IsHeytingAlgebra_612
v11
du_reflexive_728 ::
  T_IsHeytingAlgebra_612 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_728 :: T_IsHeytingAlgebra_612
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_728 T_IsHeytingAlgebra_612
v0
  = let v1 :: T_IsBoundedLattice_514
v1 = T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> T_IsHeytingAlgebra_612
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsLattice_348
v2 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsPartialOrder_248
v3 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPreorder_76
v4
                   = T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                       (T_IsPartialOrder_248 -> T_IsPartialOrder_248
forall a b. a -> b
coe T_IsPartialOrder_248
v3) in
             (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
               (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
                  (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                    ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
                       (T_IsPreorder_76 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_76
v4))
                    AgdaAny
v5))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.Eq.sym
d_sym_730 ::
  T_IsHeytingAlgebra_612 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_730 :: T_IsHeytingAlgebra_612 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_730 T_IsHeytingAlgebra_612
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360
               ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 ((T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v0))))))
-- Relation.Binary.Lattice.Structures.IsHeytingAlgebra._.Eq.trans
d_trans_732 ::
  T_IsHeytingAlgebra_612 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_732 :: T_IsHeytingAlgebra_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_732 T_IsHeytingAlgebra_612
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360
               ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 ((T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v0))))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra
d_IsBooleanAlgebra_746 :: p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsBooleanAlgebra_746 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_746
  = C_constructor_852 T_IsHeytingAlgebra_612
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._⇨_
d__'8680'__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_746 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8680'__766 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_746
-> AgdaAny
-> AgdaAny
-> AgdaAny
d__'8680'__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_746
v11 AgdaAny
v12
               AgdaAny
v13
  = (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'8680'__766 AgdaAny -> AgdaAny -> AgdaAny
v6 AgdaAny -> AgdaAny
v8 AgdaAny
v12 AgdaAny
v13
du__'8680'__766 ::
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'8680'__766 :: (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'8680'__766 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_772 ::
  T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612
d_isHeytingAlgebra_772 :: T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612
d_isHeytingAlgebra_772 T_IsBooleanAlgebra_746
v0
  = case T_IsBooleanAlgebra_746 -> T_IsBooleanAlgebra_746
forall a b. a -> b
coe T_IsBooleanAlgebra_746
v0 of
      C_constructor_852 T_IsHeytingAlgebra_612
v1 -> T_IsHeytingAlgebra_612 -> T_IsHeytingAlgebra_612
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v1
      T_IsBooleanAlgebra_746
_ -> T_IsHeytingAlgebra_612
forall a. a
MAlonzo.RTE.mazUnreachableError
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.antisym
d_antisym_776 ::
  T_IsBooleanAlgebra_746 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_776 :: T_IsBooleanAlgebra_746
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_antisym_776 T_IsBooleanAlgebra_746
v0
  = (T_IsPartialOrder_248
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPartialOrder_248
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_antisym_258
      ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360
         ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530
            ((T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 ((T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612
d_isHeytingAlgebra_772 (T_IsBooleanAlgebra_746 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_746
v0)))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.exponential
d_exponential_778 ::
  T_IsBooleanAlgebra_746 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_exponential_778 :: T_IsBooleanAlgebra_746 -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
d_exponential_778 T_IsBooleanAlgebra_746
v0
  = (T_IsHeytingAlgebra_612 -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsHeytingAlgebra_612 -> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
d_exponential_630 ((T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612
d_isHeytingAlgebra_772 (T_IsBooleanAlgebra_746 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_746
v0))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.infimum
d_infimum_780 ::
  T_IsBooleanAlgebra_746 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_infimum_780 :: T_IsBooleanAlgebra_746 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_780 T_IsBooleanAlgebra_746
v0
  = (T_IsLattice_348 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsLattice_348 -> AgdaAny -> AgdaAny -> T_Σ_14
d_infimum_364
      ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530
         ((T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 ((T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612
d_isHeytingAlgebra_772 (T_IsBooleanAlgebra_746 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_746
v0))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.isBoundedJoinSemilattice
d_isBoundedJoinSemilattice_782 ::
  MAlonzo.Code.Agda.Primitive.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_746 -> T_IsBoundedJoinSemilattice_118
d_isBoundedJoinSemilattice_782 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_746
-> T_IsBoundedJoinSemilattice_118
d_isBoundedJoinSemilattice_782 ~()
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_746
v11
  = T_IsBooleanAlgebra_746 -> T_IsBoundedJoinSemilattice_118
du_isBoundedJoinSemilattice_782 T_IsBooleanAlgebra_746
v11
du_isBoundedJoinSemilattice_782 ::
  T_IsBooleanAlgebra_746 -> T_IsBoundedJoinSemilattice_118
du_isBoundedJoinSemilattice_782 :: T_IsBooleanAlgebra_746 -> T_IsBoundedJoinSemilattice_118
du_isBoundedJoinSemilattice_782 T_IsBooleanAlgebra_746
v0
  = let v1 :: T_IsHeytingAlgebra_612
v1 = T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612
d_isHeytingAlgebra_772 (T_IsBooleanAlgebra_746 -> T_IsBooleanAlgebra_746
forall a b. a -> b
coe T_IsBooleanAlgebra_746
v0) in
    AgdaAny -> T_IsBoundedJoinSemilattice_118
forall a b. a -> b
coe
      ((T_IsBoundedLattice_514 -> T_IsBoundedJoinSemilattice_118)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBoundedLattice_514 -> T_IsBoundedJoinSemilattice_118
du_isBoundedJoinSemilattice_596
         ((T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v1)))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.isBoundedLattice
d_isBoundedLattice_784 ::
  T_IsBooleanAlgebra_746 -> T_IsBoundedLattice_514
d_isBoundedLattice_784 :: T_IsBooleanAlgebra_746 -> T_IsBoundedLattice_514
d_isBoundedLattice_784 T_IsBooleanAlgebra_746
v0
  = (T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514)
-> AgdaAny -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 ((T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612
d_isHeytingAlgebra_772 (T_IsBooleanAlgebra_746 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_746
v0))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.isBoundedMeetSemilattice
d_isBoundedMeetSemilattice_786 ::
  MAlonzo.Code.Agda.Primitive.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_746 -> T_IsBoundedMeetSemilattice_280
d_isBoundedMeetSemilattice_786 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_746
-> T_IsBoundedMeetSemilattice_280
d_isBoundedMeetSemilattice_786 ~()
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_746
v11
  = T_IsBooleanAlgebra_746 -> T_IsBoundedMeetSemilattice_280
du_isBoundedMeetSemilattice_786 T_IsBooleanAlgebra_746
v11
du_isBoundedMeetSemilattice_786 ::
  T_IsBooleanAlgebra_746 -> T_IsBoundedMeetSemilattice_280
du_isBoundedMeetSemilattice_786 :: T_IsBooleanAlgebra_746 -> T_IsBoundedMeetSemilattice_280
du_isBoundedMeetSemilattice_786 T_IsBooleanAlgebra_746
v0
  = let v1 :: T_IsHeytingAlgebra_612
v1 = T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612
d_isHeytingAlgebra_772 (T_IsBooleanAlgebra_746 -> T_IsBooleanAlgebra_746
forall a b. a -> b
coe T_IsBooleanAlgebra_746
v0) in
    AgdaAny -> T_IsBoundedMeetSemilattice_280
forall a b. a -> b
coe
      ((T_IsBoundedLattice_514 -> T_IsBoundedMeetSemilattice_280)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBoundedLattice_514 -> T_IsBoundedMeetSemilattice_280
du_isBoundedMeetSemilattice_598
         ((T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v1)))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.isEquivalence
d_isEquivalence_788 ::
  T_IsBooleanAlgebra_746 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_788 :: T_IsBooleanAlgebra_746 -> T_IsEquivalence_28
d_isEquivalence_788 T_IsBooleanAlgebra_746
v0
  = (T_IsPreorder_76 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
      T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360
            ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530
               ((T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 ((T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612
d_isHeytingAlgebra_772 (T_IsBooleanAlgebra_746 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_746
v0))))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.isJoinSemilattice
d_isJoinSemilattice_790 ::
  MAlonzo.Code.Agda.Primitive.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_746 -> T_IsJoinSemilattice_22
d_isJoinSemilattice_790 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_746
-> T_IsJoinSemilattice_22
d_isJoinSemilattice_790 ~()
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_746
v11
  = T_IsBooleanAlgebra_746 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_790 T_IsBooleanAlgebra_746
v11
du_isJoinSemilattice_790 ::
  T_IsBooleanAlgebra_746 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_790 :: T_IsBooleanAlgebra_746 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_790 T_IsBooleanAlgebra_746
v0
  = let v1 :: T_IsHeytingAlgebra_612
v1 = T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612
d_isHeytingAlgebra_772 (T_IsBooleanAlgebra_746 -> T_IsBooleanAlgebra_746
forall a b. a -> b
coe T_IsBooleanAlgebra_746
v0) in
    AgdaAny -> T_IsJoinSemilattice_22
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_514
v2 = T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> T_IsHeytingAlgebra_612
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsLattice_348 -> T_IsJoinSemilattice_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_366 ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514
v2))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.isLattice
d_isLattice_792 :: T_IsBooleanAlgebra_746 -> T_IsLattice_348
d_isLattice_792 :: T_IsBooleanAlgebra_746 -> T_IsLattice_348
d_isLattice_792 T_IsBooleanAlgebra_746
v0
  = (T_IsBoundedLattice_514 -> T_IsLattice_348)
-> AgdaAny -> T_IsLattice_348
forall a b. a -> b
coe
      T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530
      ((T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 ((T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612
d_isHeytingAlgebra_772 (T_IsBooleanAlgebra_746 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_746
v0)))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.isMeetSemilattice
d_isMeetSemilattice_794 ::
  MAlonzo.Code.Agda.Primitive.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_746 -> T_IsMeetSemilattice_184
d_isMeetSemilattice_794 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_746
-> T_IsMeetSemilattice_184
d_isMeetSemilattice_794 ~()
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_746
v11
  = T_IsBooleanAlgebra_746 -> T_IsMeetSemilattice_184
du_isMeetSemilattice_794 T_IsBooleanAlgebra_746
v11
du_isMeetSemilattice_794 ::
  T_IsBooleanAlgebra_746 -> T_IsMeetSemilattice_184
du_isMeetSemilattice_794 :: T_IsBooleanAlgebra_746 -> T_IsMeetSemilattice_184
du_isMeetSemilattice_794 T_IsBooleanAlgebra_746
v0
  = let v1 :: T_IsHeytingAlgebra_612
v1 = T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612
d_isHeytingAlgebra_772 (T_IsBooleanAlgebra_746 -> T_IsBooleanAlgebra_746
forall a b. a -> b
coe T_IsBooleanAlgebra_746
v0) in
    AgdaAny -> T_IsMeetSemilattice_184
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_514
v2 = T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> T_IsHeytingAlgebra_612
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe ((T_IsLattice_348 -> T_IsMeetSemilattice_184) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsMeetSemilattice_184
du_isMeetSemilattice_368 ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> AgdaAny
forall a b. a -> b
coe T_IsBoundedLattice_514
v2))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.isPartialOrder
d_isPartialOrder_796 ::
  T_IsBooleanAlgebra_746 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialOrder_248
d_isPartialOrder_796 :: T_IsBooleanAlgebra_746 -> T_IsPartialOrder_248
d_isPartialOrder_796 T_IsBooleanAlgebra_746
v0
  = (T_IsLattice_348 -> T_IsPartialOrder_248)
-> AgdaAny -> T_IsPartialOrder_248
forall a b. a -> b
coe
      T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360
      ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530
         ((T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 ((T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612
d_isHeytingAlgebra_772 (T_IsBooleanAlgebra_746 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_746
v0))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.isPreorder
d_isPreorder_798 ::
  T_IsBooleanAlgebra_746 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPreorder_76
d_isPreorder_798 :: T_IsBooleanAlgebra_746 -> T_IsPreorder_76
d_isPreorder_798 T_IsBooleanAlgebra_746
v0
  = (T_IsPartialOrder_248 -> T_IsPreorder_76)
-> AgdaAny -> T_IsPreorder_76
forall a b. a -> b
coe
      T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
      ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360
         ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530
            ((T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 ((T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612
d_isHeytingAlgebra_772 (T_IsBooleanAlgebra_746 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_746
v0)))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.maximum
d_maximum_800 :: T_IsBooleanAlgebra_746 -> AgdaAny -> AgdaAny
d_maximum_800 :: T_IsBooleanAlgebra_746 -> AgdaAny -> AgdaAny
d_maximum_800 T_IsBooleanAlgebra_746
v0
  = (T_IsBoundedLattice_514 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsBoundedLattice_514 -> AgdaAny -> AgdaAny
d_maximum_532
      ((T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 ((T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612
d_isHeytingAlgebra_772 (T_IsBooleanAlgebra_746 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_746
v0)))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.minimum
d_minimum_802 :: T_IsBooleanAlgebra_746 -> AgdaAny -> AgdaAny
d_minimum_802 :: T_IsBooleanAlgebra_746 -> AgdaAny -> AgdaAny
d_minimum_802 T_IsBooleanAlgebra_746
v0
  = (T_IsBoundedLattice_514 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsBoundedLattice_514 -> AgdaAny -> AgdaAny
d_minimum_534
      ((T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 ((T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612
d_isHeytingAlgebra_772 (T_IsBooleanAlgebra_746 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_746
v0)))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.refl
d_refl_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_746 -> AgdaAny -> AgdaAny
d_refl_804 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_746
-> AgdaAny
-> AgdaAny
d_refl_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_746
v11
  = T_IsBooleanAlgebra_746 -> AgdaAny -> AgdaAny
du_refl_804 T_IsBooleanAlgebra_746
v11
du_refl_804 :: T_IsBooleanAlgebra_746 -> AgdaAny -> AgdaAny
du_refl_804 :: T_IsBooleanAlgebra_746 -> AgdaAny -> AgdaAny
du_refl_804 T_IsBooleanAlgebra_746
v0
  = let v1 :: T_IsHeytingAlgebra_612
v1 = T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612
d_isHeytingAlgebra_772 (T_IsBooleanAlgebra_746 -> T_IsBooleanAlgebra_746
forall a b. a -> b
coe T_IsBooleanAlgebra_746
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_514
v2 = T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> T_IsHeytingAlgebra_612
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_348
v3 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_248
v4 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsPreorder_76 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_76 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_refl_104
                  ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                     (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v4))))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.reflexive
d_reflexive_806 ::
  T_IsBooleanAlgebra_746 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_806 :: T_IsBooleanAlgebra_746 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_reflexive_806 T_IsBooleanAlgebra_746
v0
  = (T_IsPreorder_76 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_76 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_reflexive_88
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360
            ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530
               ((T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 ((T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612
d_isHeytingAlgebra_772 (T_IsBooleanAlgebra_746 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_746
v0))))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.supremum
d_supremum_808 ::
  T_IsBooleanAlgebra_746 ->
  AgdaAny -> AgdaAny -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_supremum_808 :: T_IsBooleanAlgebra_746 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_808 T_IsBooleanAlgebra_746
v0
  = (T_IsLattice_348 -> AgdaAny -> AgdaAny -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsLattice_348 -> AgdaAny -> AgdaAny -> T_Σ_14
d_supremum_362
      ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530
         ((T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 ((T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612
d_isHeytingAlgebra_772 (T_IsBooleanAlgebra_746 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_746
v0))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.trans
d_trans_810 ::
  T_IsBooleanAlgebra_746 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_810 :: T_IsBooleanAlgebra_746
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_810 T_IsBooleanAlgebra_746
v0
  = (T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_90
      ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
         ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360
            ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530
               ((T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 ((T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612
d_isHeytingAlgebra_772 (T_IsBooleanAlgebra_746 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_746
v0))))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.transpose-⇨
d_transpose'45''8680'_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_746 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_transpose'45''8680'_812 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_746
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_transpose'45''8680'_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_746
v11
  = T_IsBooleanAlgebra_746
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8680'_812 T_IsBooleanAlgebra_746
v11
du_transpose'45''8680'_812 ::
  T_IsBooleanAlgebra_746 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8680'_812 :: T_IsBooleanAlgebra_746
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8680'_812 T_IsBooleanAlgebra_746
v0
  = (T_IsHeytingAlgebra_612
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsHeytingAlgebra_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8680'_638 ((T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612
d_isHeytingAlgebra_772 (T_IsBooleanAlgebra_746 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_746
v0))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.transpose-∧
d_transpose'45''8743'_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_746 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_transpose'45''8743'_814 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_746
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_transpose'45''8743'_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_746
v11
  = T_IsBooleanAlgebra_746
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8743'_814 T_IsBooleanAlgebra_746
v11
du_transpose'45''8743'_814 ::
  T_IsBooleanAlgebra_746 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8743'_814 :: T_IsBooleanAlgebra_746
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8743'_814 T_IsBooleanAlgebra_746
v0
  = (T_IsHeytingAlgebra_612
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsHeytingAlgebra_612
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_transpose'45''8743'_654 ((T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612
d_isHeytingAlgebra_772 (T_IsBooleanAlgebra_746 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_746
v0))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.x∧y≤x
d_x'8743'y'8804'x_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_746 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'x_816 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_746
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'x_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_746
v11
  = T_IsBooleanAlgebra_746 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_816 T_IsBooleanAlgebra_746
v11
du_x'8743'y'8804'x_816 ::
  T_IsBooleanAlgebra_746 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_816 :: T_IsBooleanAlgebra_746 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_816 T_IsBooleanAlgebra_746
v0
  = let v1 :: T_IsHeytingAlgebra_612
v1 = T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612
d_isHeytingAlgebra_772 (T_IsBooleanAlgebra_746 -> T_IsBooleanAlgebra_746
forall a b. a -> b
coe T_IsBooleanAlgebra_746
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_514
v2 = T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> T_IsHeytingAlgebra_612
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_348
v3 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'x_200 ((T_IsLattice_348 -> T_IsMeetSemilattice_184) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsMeetSemilattice_184
du_isMeetSemilattice_368 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v3)))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.x∧y≤y
d_x'8743'y'8804'y_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_746 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8743'y'8804'y_818 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_746
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8743'y'8804'y_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_746
v11
  = T_IsBooleanAlgebra_746 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_818 T_IsBooleanAlgebra_746
v11
du_x'8743'y'8804'y_818 ::
  T_IsBooleanAlgebra_746 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_818 :: T_IsBooleanAlgebra_746 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_818 T_IsBooleanAlgebra_746
v0
  = let v1 :: T_IsHeytingAlgebra_612
v1 = T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612
d_isHeytingAlgebra_772 (T_IsBooleanAlgebra_746 -> T_IsBooleanAlgebra_746
forall a b. a -> b
coe T_IsBooleanAlgebra_746
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_514
v2 = T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> T_IsHeytingAlgebra_612
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_348
v3 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMeetSemilattice_184 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8743'y'8804'y_212 ((T_IsLattice_348 -> T_IsMeetSemilattice_184) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsMeetSemilattice_184
du_isMeetSemilattice_368 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v3)))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.x≤x∨y
d_x'8804'x'8744'y_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_746 -> AgdaAny -> AgdaAny -> AgdaAny
d_x'8804'x'8744'y_820 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_746
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_x'8804'x'8744'y_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_746
v11
  = T_IsBooleanAlgebra_746 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_820 T_IsBooleanAlgebra_746
v11
du_x'8804'x'8744'y_820 ::
  T_IsBooleanAlgebra_746 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_820 :: T_IsBooleanAlgebra_746 -> AgdaAny -> AgdaAny -> AgdaAny
du_x'8804'x'8744'y_820 T_IsBooleanAlgebra_746
v0
  = let v1 :: T_IsHeytingAlgebra_612
v1 = T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612
d_isHeytingAlgebra_772 (T_IsBooleanAlgebra_746 -> T_IsBooleanAlgebra_746
forall a b. a -> b
coe T_IsBooleanAlgebra_746
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_514
v2 = T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> T_IsHeytingAlgebra_612
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_348
v3 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
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_348 -> T_IsJoinSemilattice_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_366 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v3)))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.y≤x∨y
d_y'8804'x'8744'y_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_746 -> AgdaAny -> AgdaAny -> AgdaAny
d_y'8804'x'8744'y_822 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_746
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_y'8804'x'8744'y_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_746
v11
  = T_IsBooleanAlgebra_746 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_822 T_IsBooleanAlgebra_746
v11
du_y'8804'x'8744'y_822 ::
  T_IsBooleanAlgebra_746 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_822 :: T_IsBooleanAlgebra_746 -> AgdaAny -> AgdaAny -> AgdaAny
du_y'8804'x'8744'y_822 T_IsBooleanAlgebra_746
v0
  = let v1 :: T_IsHeytingAlgebra_612
v1 = T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612
d_isHeytingAlgebra_772 (T_IsBooleanAlgebra_746 -> T_IsBooleanAlgebra_746
forall a b. a -> b
coe T_IsBooleanAlgebra_746
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_514
v2 = T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> T_IsHeytingAlgebra_612
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_348
v3 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
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_348 -> T_IsJoinSemilattice_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_366 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v3)))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.∧-greatest
d_'8743''45'greatest_824 ::
  MAlonzo.Code.Agda.Primitive.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_746 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'greatest_824 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_746
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'greatest_824 ~()
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_746
v11
  = T_IsBooleanAlgebra_746
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_824 T_IsBooleanAlgebra_746
v11
du_'8743''45'greatest_824 ::
  T_IsBooleanAlgebra_746 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_824 :: T_IsBooleanAlgebra_746
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_824 T_IsBooleanAlgebra_746
v0
  = let v1 :: T_IsHeytingAlgebra_612
v1 = T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612
d_isHeytingAlgebra_772 (T_IsBooleanAlgebra_746 -> T_IsBooleanAlgebra_746
forall a b. a -> b
coe T_IsBooleanAlgebra_746
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_514
v2 = T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> T_IsHeytingAlgebra_612
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_348
v3 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            ((T_IsMeetSemilattice_184
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsMeetSemilattice_184
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'greatest_226
               ((T_IsLattice_348 -> T_IsMeetSemilattice_184) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsMeetSemilattice_184
du_isMeetSemilattice_368 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v3)))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.∨-least
d_'8744''45'least_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_746 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8744''45'least_826 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_746
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8744''45'least_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_746
v11
  = T_IsBooleanAlgebra_746
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_826 T_IsBooleanAlgebra_746
v11
du_'8744''45'least_826 ::
  T_IsBooleanAlgebra_746 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_826 :: T_IsBooleanAlgebra_746
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8744''45'least_826 T_IsBooleanAlgebra_746
v0
  = let v1 :: T_IsHeytingAlgebra_612
v1 = T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612
d_isHeytingAlgebra_772 (T_IsBooleanAlgebra_746 -> T_IsBooleanAlgebra_746
forall a b. a -> b
coe T_IsBooleanAlgebra_746
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_514
v2 = T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> T_IsHeytingAlgebra_612
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_348
v3 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
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_348 -> T_IsJoinSemilattice_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348 -> T_IsJoinSemilattice_22
du_isJoinSemilattice_366 (T_IsLattice_348 -> AgdaAny
forall a b. a -> b
coe T_IsLattice_348
v3)))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.∼-resp-≈
d_'8764''45'resp'45''8776'_828 ::
  MAlonzo.Code.Agda.Primitive.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_746 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8764''45'resp'45''8776'_828 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_746
-> T_Σ_14
d_'8764''45'resp'45''8776'_828 ~()
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_746
v11
  = T_IsBooleanAlgebra_746 -> T_Σ_14
du_'8764''45'resp'45''8776'_828 T_IsBooleanAlgebra_746
v11
du_'8764''45'resp'45''8776'_828 ::
  T_IsBooleanAlgebra_746 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8764''45'resp'45''8776'_828 :: T_IsBooleanAlgebra_746 -> T_Σ_14
du_'8764''45'resp'45''8776'_828 T_IsBooleanAlgebra_746
v0
  = let v1 :: T_IsHeytingAlgebra_612
v1 = T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612
d_isHeytingAlgebra_772 (T_IsBooleanAlgebra_746 -> T_IsBooleanAlgebra_746
forall a b. a -> b
coe T_IsBooleanAlgebra_746
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_514
v2 = T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> T_IsHeytingAlgebra_612
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_348
v3 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_248
v4 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsPreorder_76 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_76 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'45''8776'_124
                  ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                     (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v4))))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.∼-respʳ-≈
d_'8764''45'resp'691''45''8776'_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_746 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'691''45''8776'_830 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_746
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'691''45''8776'_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_746
v11
  = T_IsBooleanAlgebra_746
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_830 T_IsBooleanAlgebra_746
v11
du_'8764''45'resp'691''45''8776'_830 ::
  T_IsBooleanAlgebra_746 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_830 :: T_IsBooleanAlgebra_746
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'691''45''8776'_830 T_IsBooleanAlgebra_746
v0
  = let v1 :: T_IsHeytingAlgebra_612
v1 = T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612
d_isHeytingAlgebra_772 (T_IsBooleanAlgebra_746 -> T_IsBooleanAlgebra_746
forall a b. a -> b
coe T_IsBooleanAlgebra_746
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_514
v2 = T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> T_IsHeytingAlgebra_612
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_348
v3 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_248
v4 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'691''45''8776'_122
                  ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                     (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v4))))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.∼-respˡ-≈
d_'8764''45'resp'737''45''8776'_832 ::
  MAlonzo.Code.Agda.Primitive.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_746 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8764''45'resp'737''45''8776'_832 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_746
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8764''45'resp'737''45''8776'_832 ~()
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_746
v11
  = T_IsBooleanAlgebra_746
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_832 T_IsBooleanAlgebra_746
v11
du_'8764''45'resp'737''45''8776'_832 ::
  T_IsBooleanAlgebra_746 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_832 :: T_IsBooleanAlgebra_746
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8764''45'resp'737''45''8776'_832 T_IsBooleanAlgebra_746
v0
  = let v1 :: T_IsHeytingAlgebra_612
v1 = T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612
d_isHeytingAlgebra_772 (T_IsBooleanAlgebra_746 -> T_IsBooleanAlgebra_746
forall a b. a -> b
coe T_IsBooleanAlgebra_746
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_514
v2 = T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> T_IsHeytingAlgebra_612
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_348
v3 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_248
v4 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8764''45'resp'737''45''8776'_120
                  ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                     (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v4))))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.≲-resp-≈
d_'8818''45'resp'45''8776'_834 ::
  MAlonzo.Code.Agda.Primitive.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_746 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8818''45'resp'45''8776'_834 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_746
-> T_Σ_14
d_'8818''45'resp'45''8776'_834 ~()
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_746
v11
  = T_IsBooleanAlgebra_746 -> T_Σ_14
du_'8818''45'resp'45''8776'_834 T_IsBooleanAlgebra_746
v11
du_'8818''45'resp'45''8776'_834 ::
  T_IsBooleanAlgebra_746 -> MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8818''45'resp'45''8776'_834 :: T_IsBooleanAlgebra_746 -> T_Σ_14
du_'8818''45'resp'45''8776'_834 T_IsBooleanAlgebra_746
v0
  = let v1 :: T_IsHeytingAlgebra_612
v1 = T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612
d_isHeytingAlgebra_772 (T_IsBooleanAlgebra_746 -> T_IsBooleanAlgebra_746
forall a b. a -> b
coe T_IsBooleanAlgebra_746
v0) in
    AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_514
v2 = T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> T_IsHeytingAlgebra_612
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_348
v3 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_248
v4 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsPreorder_76 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_76 -> T_Σ_14
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'45''8776'_118
                  ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                     (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v4))))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.≲-respʳ-≈
d_'8818''45'resp'691''45''8776'_836 ::
  MAlonzo.Code.Agda.Primitive.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_746 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'691''45''8776'_836 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_746
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'691''45''8776'_836 ~()
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_746
v11
  = T_IsBooleanAlgebra_746
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_836 T_IsBooleanAlgebra_746
v11
du_'8818''45'resp'691''45''8776'_836 ::
  T_IsBooleanAlgebra_746 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_836 :: T_IsBooleanAlgebra_746
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'691''45''8776'_836 T_IsBooleanAlgebra_746
v0
  = let v1 :: T_IsHeytingAlgebra_612
v1 = T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612
d_isHeytingAlgebra_772 (T_IsBooleanAlgebra_746 -> T_IsBooleanAlgebra_746
forall a b. a -> b
coe T_IsBooleanAlgebra_746
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_514
v2 = T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> T_IsHeytingAlgebra_612
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_348
v3 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_248
v4 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'691''45''8776'_112
                  ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                     (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v4))))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.≲-respˡ-≈
d_'8818''45'resp'737''45''8776'_838 ::
  MAlonzo.Code.Agda.Primitive.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_746 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8818''45'resp'737''45''8776'_838 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_746
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8818''45'resp'737''45''8776'_838 ~()
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_746
v11
  = T_IsBooleanAlgebra_746
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_838 T_IsBooleanAlgebra_746
v11
du_'8818''45'resp'737''45''8776'_838 ::
  T_IsBooleanAlgebra_746 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_838 :: T_IsBooleanAlgebra_746
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8818''45'resp'737''45''8776'_838 T_IsBooleanAlgebra_746
v0
  = let v1 :: T_IsHeytingAlgebra_612
v1 = T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612
d_isHeytingAlgebra_772 (T_IsBooleanAlgebra_746 -> T_IsBooleanAlgebra_746
forall a b. a -> b
coe T_IsBooleanAlgebra_746
v0) in
    AgdaAny
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_514
v2 = T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> T_IsHeytingAlgebra_612
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_348
v3 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_248
v4 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               ((T_IsPreorder_76
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsPreorder_76
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_'8818''45'resp'737''45''8776'_106
                  ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                     (T_IsPartialOrder_248 -> AgdaAny
forall a b. a -> b
coe T_IsPartialOrder_248
v4))))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.Eq.isPartialEquivalence
d_isPartialEquivalence_842 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsBooleanAlgebra_746 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
d_isPartialEquivalence_842 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_746
-> T_IsPartialEquivalence_16
d_isPartialEquivalence_842 ~()
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_746
v11
  = T_IsBooleanAlgebra_746 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_842 T_IsBooleanAlgebra_746
v11
du_isPartialEquivalence_842 ::
  T_IsBooleanAlgebra_746 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsPartialEquivalence_16
du_isPartialEquivalence_842 :: T_IsBooleanAlgebra_746 -> T_IsPartialEquivalence_16
du_isPartialEquivalence_842 T_IsBooleanAlgebra_746
v0
  = let v1 :: T_IsHeytingAlgebra_612
v1 = T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612
d_isHeytingAlgebra_772 (T_IsBooleanAlgebra_746 -> T_IsBooleanAlgebra_746
forall a b. a -> b
coe T_IsBooleanAlgebra_746
v0) in
    AgdaAny -> T_IsPartialEquivalence_16
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_514
v2 = T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> T_IsHeytingAlgebra_612
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_348
v3 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_248
v4 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPreorder_76
v5
                      = T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                          (T_IsPartialOrder_248 -> T_IsPartialOrder_248
forall a b. a -> b
coe T_IsPartialOrder_248
v4) in
                AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  ((T_IsEquivalence_28 -> T_IsPartialEquivalence_16)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> T_IsPartialEquivalence_16
MAlonzo.Code.Relation.Binary.Structures.du_isPartialEquivalence_44
                     ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
                        (T_IsPreorder_76 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_76
v5)))))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.Eq.refl
d_refl_844 :: T_IsBooleanAlgebra_746 -> AgdaAny -> AgdaAny
d_refl_844 :: T_IsBooleanAlgebra_746 -> AgdaAny -> AgdaAny
d_refl_844 T_IsBooleanAlgebra_746
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360
               ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530
                  ((T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 ((T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612
d_isHeytingAlgebra_772 (T_IsBooleanAlgebra_746 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_746
v0)))))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.Eq.reflexive
d_reflexive_846 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  () ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> ()) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny ->
  T_IsBooleanAlgebra_746 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
d_reflexive_846 :: ()
-> ()
-> ()
-> ()
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> ())
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_746
-> AgdaAny
-> AgdaAny
-> T__'8801'__12
-> AgdaAny
d_reflexive_846 ~()
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_746
v11
  = T_IsBooleanAlgebra_746
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_846 T_IsBooleanAlgebra_746
v11
du_reflexive_846 ::
  T_IsBooleanAlgebra_746 ->
  AgdaAny ->
  AgdaAny ->
  MAlonzo.Code.Agda.Builtin.Equality.T__'8801'__12 -> AgdaAny
du_reflexive_846 :: T_IsBooleanAlgebra_746
-> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
du_reflexive_846 T_IsBooleanAlgebra_746
v0
  = let v1 :: T_IsHeytingAlgebra_612
v1 = T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612
d_isHeytingAlgebra_772 (T_IsBooleanAlgebra_746 -> T_IsBooleanAlgebra_746
forall a b. a -> b
coe T_IsBooleanAlgebra_746
v0) in
    AgdaAny -> AgdaAny -> AgdaAny -> T__'8801'__12 -> AgdaAny
forall a b. a -> b
coe
      (let v2 :: T_IsBoundedLattice_514
v2 = T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 (T_IsHeytingAlgebra_612 -> T_IsHeytingAlgebra_612
forall a b. a -> b
coe T_IsHeytingAlgebra_612
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         (let v3 :: T_IsLattice_348
v3 = T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530 (T_IsBoundedLattice_514 -> T_IsBoundedLattice_514
forall a b. a -> b
coe T_IsBoundedLattice_514
v2) in
          AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (let v4 :: T_IsPartialOrder_248
v4 = T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360 (T_IsLattice_348 -> T_IsLattice_348
forall a b. a -> b
coe T_IsLattice_348
v3) in
             AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (let v5 :: T_IsPreorder_76
v5
                      = T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
                          (T_IsPartialOrder_248 -> T_IsPartialOrder_248
forall a b. a -> b
coe T_IsPartialOrder_248
v4) in
                (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
                  (\ AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 ->
                     (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.du_reflexive_42
                       ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
                          (T_IsPreorder_76 -> AgdaAny
forall a b. a -> b
coe T_IsPreorder_76
v5))
                       AgdaAny
v6)))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.Eq.sym
d_sym_848 ::
  T_IsBooleanAlgebra_746 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_848 :: T_IsBooleanAlgebra_746 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_sym_848 T_IsBooleanAlgebra_746
v0
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360
               ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530
                  ((T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 ((T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612
d_isHeytingAlgebra_772 (T_IsBooleanAlgebra_746 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_746
v0)))))))
-- Relation.Binary.Lattice.Structures.IsBooleanAlgebra._.Eq.trans
d_trans_850 ::
  T_IsBooleanAlgebra_746 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_850 :: T_IsBooleanAlgebra_746
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_trans_850 T_IsBooleanAlgebra_746
v0
  = (T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
      ((T_IsPreorder_76 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsPreorder_76 -> T_IsEquivalence_28
MAlonzo.Code.Relation.Binary.Structures.d_isEquivalence_86
         ((T_IsPartialOrder_248 -> T_IsPreorder_76) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsPartialOrder_248 -> T_IsPreorder_76
MAlonzo.Code.Relation.Binary.Structures.d_isPreorder_256
            ((T_IsLattice_348 -> T_IsPartialOrder_248) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_348 -> T_IsPartialOrder_248
d_isPartialOrder_360
               ((T_IsBoundedLattice_514 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBoundedLattice_514 -> T_IsLattice_348
d_isLattice_530
                  ((T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsHeytingAlgebra_612 -> T_IsBoundedLattice_514
d_isBoundedLattice_628 ((T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_746 -> T_IsHeytingAlgebra_612
d_isHeytingAlgebra_772 (T_IsBooleanAlgebra_746 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_746
v0)))))))