{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE EmptyCase #-}
{-# LANGUAGE EmptyDataDecls #-}
{-# LANGUAGE ExistentialQuantification #-}
{-# LANGUAGE NoMonomorphismRestriction #-}
{-# LANGUAGE OverloadedStrings #-}
{-# LANGUAGE PatternSynonyms #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE ScopedTypeVariables #-}

{-# OPTIONS_GHC -Wno-overlapping-patterns #-}

module MAlonzo.Code.Algebra.Lattice.Properties.BooleanAlgebra 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.Sigma
import qualified MAlonzo.Code.Agda.Primitive
import qualified MAlonzo.Code.Algebra.Bundles
import qualified MAlonzo.Code.Algebra.Consequences.Setoid
import qualified MAlonzo.Code.Algebra.Lattice.Bundles
import qualified MAlonzo.Code.Algebra.Lattice.Properties.DistributiveLattice
import qualified MAlonzo.Code.Algebra.Lattice.Properties.Lattice
import qualified MAlonzo.Code.Algebra.Lattice.Properties.Semilattice
import qualified MAlonzo.Code.Algebra.Lattice.Structures
import qualified MAlonzo.Code.Algebra.Structures
import qualified MAlonzo.Code.Function.Base
import qualified MAlonzo.Code.Relation.Binary.Bundles
import qualified MAlonzo.Code.Relation.Binary.Lattice.Bundles
import qualified MAlonzo.Code.Relation.Binary.Lattice.Structures
import qualified MAlonzo.Code.Relation.Binary.Reasoning.Base.Single
import qualified MAlonzo.Code.Relation.Binary.Reasoning.Syntax
import qualified MAlonzo.Code.Relation.Binary.Structures

-- Algebra.Lattice.Properties.BooleanAlgebra._.IsAbelianGroup
d_IsAbelianGroup_116 :: p -> p -> p -> p -> p -> p -> ()
d_IsAbelianGroup_116 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
-- Algebra.Lattice.Properties.BooleanAlgebra._.IsCommutativeMonoid
d_IsCommutativeMonoid_140 :: p -> p -> p -> p -> p -> ()
d_IsCommutativeMonoid_140 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
-- Algebra.Lattice.Properties.BooleanAlgebra._.IsCommutativeRing
d_IsCommutativeRing_144 :: p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsCommutativeRing_144 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 = ()
-- Algebra.Lattice.Properties.BooleanAlgebra._.IsCommutativeSemiring
d_IsCommutativeSemiring_152 :: p -> p -> p -> p -> p -> p -> p -> ()
d_IsCommutativeSemiring_152 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Lattice.Properties.BooleanAlgebra._.IsGroup
d_IsGroup_164 :: p -> p -> p -> p -> p -> p -> ()
d_IsGroup_164 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 = ()
-- Algebra.Lattice.Properties.BooleanAlgebra._.IsMagma
d_IsMagma_204 :: p -> p -> p -> p -> ()
d_IsMagma_204 p
a0 p
a1 p
a2 p
a3 = ()
-- Algebra.Lattice.Properties.BooleanAlgebra._.IsMonoid
d_IsMonoid_216 :: p -> p -> p -> p -> p -> ()
d_IsMonoid_216 p
a0 p
a1 p
a2 p
a3 p
a4 = ()
-- Algebra.Lattice.Properties.BooleanAlgebra._.IsRing
d_IsRing_248 :: p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsRing_248 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 = ()
-- Algebra.Lattice.Properties.BooleanAlgebra._.IsSemigroup
d_IsSemigroup_260 :: p -> p -> p -> p -> ()
d_IsSemigroup_260 p
a0 p
a1 p
a2 p
a3 = ()
-- Algebra.Lattice.Properties.BooleanAlgebra._.IsSemiring
d_IsSemiring_268 :: p -> p -> p -> p -> p -> p -> p -> ()
d_IsSemiring_268 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 = ()
-- Algebra.Lattice.Properties.BooleanAlgebra._.IsAbelianGroup.comm
d_comm_294 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_comm_294 :: T_IsAbelianGroup_1172 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_294 T_IsAbelianGroup_1172
v0
  = (T_IsAbelianGroup_1172 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_1186 (T_IsAbelianGroup_1172 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0)
-- Algebra.Lattice.Properties.BooleanAlgebra._.IsAbelianGroup.isGroup
d_isGroup_316 ::
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172 ->
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074
d_isGroup_316 :: T_IsAbelianGroup_1172 -> T_IsGroup_1074
d_isGroup_316 T_IsAbelianGroup_1172
v0
  = (T_IsAbelianGroup_1172 -> T_IsGroup_1074)
-> AgdaAny -> T_IsGroup_1074
forall a b. a -> b
coe T_IsAbelianGroup_1172 -> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.d_isGroup_1184 (T_IsAbelianGroup_1172 -> AgdaAny
forall a b. a -> b
coe T_IsAbelianGroup_1172
v0)
-- Algebra.Lattice.Properties.BooleanAlgebra._.IsCommutativeMonoid.comm
d_comm_584 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_comm_584 :: T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny -> AgdaAny
d_comm_584 T_IsCommutativeMonoid_764
v0
  = (T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_comm_776 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v0)
-- Algebra.Lattice.Properties.BooleanAlgebra._.IsCommutativeMonoid.isMonoid
d_isMonoid_600 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_isMonoid_600 :: T_IsCommutativeMonoid_764 -> T_IsMonoid_712
d_isMonoid_600 T_IsCommutativeMonoid_764
v0
  = (T_IsCommutativeMonoid_764 -> T_IsMonoid_712)
-> AgdaAny -> T_IsMonoid_712
forall a b. a -> b
coe T_IsCommutativeMonoid_764 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_774 (T_IsCommutativeMonoid_764 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeMonoid_764
v0)
-- Algebra.Lattice.Properties.BooleanAlgebra._.IsCommutativeRing.*-comm
d_'42''45'comm_630 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_630 :: T_IsCommutativeRing_2888 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_630 T_IsCommutativeRing_2888
v0
  = (T_IsCommutativeRing_2888 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2888 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'comm_2906 (T_IsCommutativeRing_2888 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2888
v0)
-- Algebra.Lattice.Properties.BooleanAlgebra._.IsCommutativeRing.isRing
d_isRing_718 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888 ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740
d_isRing_718 :: T_IsCommutativeRing_2888 -> T_IsRing_2740
d_isRing_718 T_IsCommutativeRing_2888
v0
  = (T_IsCommutativeRing_2888 -> T_IsRing_2740)
-> AgdaAny -> T_IsRing_2740
forall a b. a -> b
coe T_IsCommutativeRing_2888 -> T_IsRing_2740
MAlonzo.Code.Algebra.Structures.d_isRing_2904 (T_IsCommutativeRing_2888 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeRing_2888
v0)
-- Algebra.Lattice.Properties.BooleanAlgebra._.IsCommutativeSemiring.*-comm
d_'42''45'comm_784 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_784 :: T_IsCommutativeSemiring_1750 -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'comm_784 T_IsCommutativeSemiring_1750
v0
  = (T_IsCommutativeSemiring_1750 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1750 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'comm_1766 (T_IsCommutativeSemiring_1750 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1750
v0)
-- Algebra.Lattice.Properties.BooleanAlgebra._.IsCommutativeSemiring.isSemiring
d_isSemiring_854 ::
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640
d_isSemiring_854 :: T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
d_isSemiring_854 T_IsCommutativeSemiring_1750
v0
  = (T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640)
-> AgdaAny -> T_IsSemiring_1640
forall a b. a -> b
coe T_IsCommutativeSemiring_1750 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.d_isSemiring_1764 (T_IsCommutativeSemiring_1750 -> AgdaAny
forall a b. a -> b
coe T_IsCommutativeSemiring_1750
v0)
-- Algebra.Lattice.Properties.BooleanAlgebra._.IsGroup.inverse
d_inverse_992 ::
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_inverse_992 :: T_IsGroup_1074 -> T_Σ_14
d_inverse_992 T_IsGroup_1074
v0
  = (T_IsGroup_1074 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsGroup_1074 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_inverse_1090 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v0)
-- Algebra.Lattice.Properties.BooleanAlgebra._.IsGroup.isMonoid
d_isMonoid_1006 ::
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_isMonoid_1006 :: T_IsGroup_1074 -> T_IsMonoid_712
d_isMonoid_1006 T_IsGroup_1074
v0
  = (T_IsGroup_1074 -> T_IsMonoid_712) -> AgdaAny -> T_IsMonoid_712
forall a b. a -> b
coe T_IsGroup_1074 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.d_isMonoid_1088 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v0)
-- Algebra.Lattice.Properties.BooleanAlgebra._.IsGroup.⁻¹-cong
d_'8315''185''45'cong_1028 ::
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1028 :: T_IsGroup_1074 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8315''185''45'cong_1028 T_IsGroup_1074
v0
  = (T_IsGroup_1074 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsGroup_1074 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8315''185''45'cong_1092 (T_IsGroup_1074 -> AgdaAny
forall a b. a -> b
coe T_IsGroup_1074
v0)
-- Algebra.Lattice.Properties.BooleanAlgebra._.IsMagma.isEquivalence
d_isEquivalence_1556 ::
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178 ->
  MAlonzo.Code.Relation.Binary.Structures.T_IsEquivalence_28
d_isEquivalence_1556 :: T_IsMagma_178 -> T_IsEquivalence_28
d_isEquivalence_1556 T_IsMagma_178
v0
  = (T_IsMagma_178 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe T_IsMagma_178 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Structures.d_isEquivalence_186 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v0)
-- Algebra.Lattice.Properties.BooleanAlgebra._.IsMagma.∙-cong
d_'8729''45'cong_1570 ::
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8729''45'cong_1570 :: T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8729''45'cong_1570 T_IsMagma_178
v0
  = (T_IsMagma_178
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'8729''45'cong_188 (T_IsMagma_178 -> AgdaAny
forall a b. a -> b
coe T_IsMagma_178
v0)
-- Algebra.Lattice.Properties.BooleanAlgebra._.IsMonoid.identity
d_identity_1666 ::
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_identity_1666 :: T_IsMonoid_712 -> T_Σ_14
d_identity_1666 T_IsMonoid_712
v0
  = (T_IsMonoid_712 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsMonoid_712 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_identity_724 (T_IsMonoid_712 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712
v0)
-- Algebra.Lattice.Properties.BooleanAlgebra._.IsMonoid.isSemigroup
d_isSemigroup_1678 ::
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_isSemigroup_1678 :: T_IsMonoid_712 -> T_IsSemigroup_488
d_isSemigroup_1678 T_IsMonoid_712
v0
  = (T_IsMonoid_712 -> T_IsSemigroup_488)
-> AgdaAny -> T_IsSemigroup_488
forall a b. a -> b
coe T_IsMonoid_712 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.d_isSemigroup_722 (T_IsMonoid_712 -> AgdaAny
forall a b. a -> b
coe T_IsMonoid_712
v0)
-- Algebra.Lattice.Properties.BooleanAlgebra._.IsRing.*-assoc
d_'42''45'assoc_2184 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_2184 :: T_IsRing_2740 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'assoc_2184 T_IsRing_2740
v0
  = (T_IsRing_2740 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsRing_2740 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'assoc_2766 (T_IsRing_2740 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2740
v0)
-- Algebra.Lattice.Properties.BooleanAlgebra._.IsRing.*-cong
d_'42''45'cong_2186 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'42''45'cong_2186 :: T_IsRing_2740
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'42''45'cong_2186 T_IsRing_2740
v0
  = (T_IsRing_2740
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe T_IsRing_2740
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Structures.d_'42''45'cong_2764 (T_IsRing_2740 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2740
v0)
-- Algebra.Lattice.Properties.BooleanAlgebra._.IsRing.*-identity
d_'42''45'identity_2192 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'42''45'identity_2192 :: T_IsRing_2740 -> T_Σ_14
d_'42''45'identity_2192 T_IsRing_2740
v0
  = (T_IsRing_2740 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsRing_2740 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_'42''45'identity_2768 (T_IsRing_2740 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2740
v0)
-- Algebra.Lattice.Properties.BooleanAlgebra._.IsRing.+-isAbelianGroup
d_'43''45'isAbelianGroup_2220 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172
d_'43''45'isAbelianGroup_2220 :: T_IsRing_2740 -> T_IsAbelianGroup_1172
d_'43''45'isAbelianGroup_2220 T_IsRing_2740
v0
  = (T_IsRing_2740 -> T_IsAbelianGroup_1172)
-> AgdaAny -> T_IsAbelianGroup_1172
forall a b. a -> b
coe
      T_IsRing_2740 -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.d_'43''45'isAbelianGroup_2762
      (T_IsRing_2740 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2740
v0)
-- Algebra.Lattice.Properties.BooleanAlgebra._.IsRing.distrib
d_distrib_2250 ::
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_distrib_2250 :: T_IsRing_2740 -> T_Σ_14
d_distrib_2250 T_IsRing_2740
v0
  = (T_IsRing_2740 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsRing_2740 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_distrib_2770 (T_IsRing_2740 -> AgdaAny
forall a b. a -> b
coe T_IsRing_2740
v0)
-- Algebra.Lattice.Properties.BooleanAlgebra._.IsSemigroup.assoc
d_assoc_2412 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2412 :: T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_assoc_2412 T_IsSemigroup_488
v0
  = (T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Structures.d_assoc_498 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v0)
-- Algebra.Lattice.Properties.BooleanAlgebra._.IsSemigroup.isMagma
d_isMagma_2416 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_isMagma_2416 :: T_IsSemigroup_488 -> T_IsMagma_178
d_isMagma_2416 T_IsSemigroup_488
v0
  = (T_IsSemigroup_488 -> T_IsMagma_178) -> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe T_IsSemigroup_488 -> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.d_isMagma_496 (T_IsSemigroup_488 -> AgdaAny
forall a b. a -> b
coe T_IsSemigroup_488
v0)
-- Algebra.Lattice.Properties.BooleanAlgebra._.IsSemiring.isSemiringWithoutAnnihilatingZero
d_isSemiringWithoutAnnihilatingZero_2530 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiringWithoutAnnihilatingZero_1536
d_isSemiringWithoutAnnihilatingZero_2530 :: T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
d_isSemiringWithoutAnnihilatingZero_2530 T_IsSemiring_1640
v0
  = (T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> AgdaAny -> T_IsSemiringWithoutAnnihilatingZero_1536
forall a b. a -> b
coe
      T_IsSemiring_1640 -> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.d_isSemiringWithoutAnnihilatingZero_1654
      (T_IsSemiring_1640 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1640
v0)
-- Algebra.Lattice.Properties.BooleanAlgebra._.IsSemiring.zero
d_zero_2544 ::
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_zero_2544 :: T_IsSemiring_1640 -> T_Σ_14
d_zero_2544 T_IsSemiring_1640
v0
  = (T_IsSemiring_1640 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe T_IsSemiring_1640 -> T_Σ_14
MAlonzo.Code.Algebra.Structures.d_zero_1656 (T_IsSemiring_1640 -> AgdaAny
forall a b. a -> b
coe T_IsSemiring_1640
v0)
-- Algebra.Lattice.Properties.BooleanAlgebra._._DistributesOver_
d__DistributesOver__2740 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d__DistributesOver__2740 :: ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
d__DistributesOver__2740 = ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
forall a. a
erased
-- Algebra.Lattice.Properties.BooleanAlgebra._._DistributesOverʳ_
d__DistributesOver'691'__2742 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d__DistributesOver'691'__2742 :: ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
d__DistributesOver'691'__2742 = ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
forall a. a
erased
-- Algebra.Lattice.Properties.BooleanAlgebra._._DistributesOverˡ_
d__DistributesOver'737'__2744 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d__DistributesOver'737'__2744 :: ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
d__DistributesOver'737'__2744 = ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
forall a. a
erased
-- Algebra.Lattice.Properties.BooleanAlgebra._.Associative
d_Associative_2760 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Associative_2760 :: ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
d_Associative_2760 = ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
forall a. a
erased
-- Algebra.Lattice.Properties.BooleanAlgebra._.Commutative
d_Commutative_2764 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Commutative_2764 :: ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
d_Commutative_2764 = ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
forall a. a
erased
-- Algebra.Lattice.Properties.BooleanAlgebra._.Congruent₂
d_Congruent'8322'_2768 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Congruent'8322'_2768 :: ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
d_Congruent'8322'_2768 = ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
forall a. a
erased
-- Algebra.Lattice.Properties.BooleanAlgebra._.Identity
d_Identity_2780 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Identity_2780 :: ()
-> ()
-> T_BooleanAlgebra_698
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
d_Identity_2780 = ()
-> ()
-> T_BooleanAlgebra_698
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
forall a. a
erased
-- Algebra.Lattice.Properties.BooleanAlgebra._.Inverse
d_Inverse_2784 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Inverse_2784 :: ()
-> ()
-> T_BooleanAlgebra_698
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
d_Inverse_2784 = ()
-> ()
-> T_BooleanAlgebra_698
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
forall a. a
erased
-- Algebra.Lattice.Properties.BooleanAlgebra._.Involutive
d_Involutive_2788 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny) -> ()
d_Involutive_2788 :: () -> () -> T_BooleanAlgebra_698 -> (AgdaAny -> AgdaAny) -> ()
d_Involutive_2788 = () -> () -> T_BooleanAlgebra_698 -> (AgdaAny -> AgdaAny) -> ()
forall a. a
erased
-- Algebra.Lattice.Properties.BooleanAlgebra._.LeftIdentity
d_LeftIdentity_2806 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_LeftIdentity_2806 :: ()
-> ()
-> T_BooleanAlgebra_698
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
d_LeftIdentity_2806 = ()
-> ()
-> T_BooleanAlgebra_698
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
forall a. a
erased
-- Algebra.Lattice.Properties.BooleanAlgebra._.LeftInverse
d_LeftInverse_2808 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_LeftInverse_2808 :: ()
-> ()
-> T_BooleanAlgebra_698
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
d_LeftInverse_2808 = ()
-> ()
-> T_BooleanAlgebra_698
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
forall a. a
erased
-- Algebra.Lattice.Properties.BooleanAlgebra._.LeftZero
d_LeftZero_2814 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_LeftZero_2814 :: ()
-> ()
-> T_BooleanAlgebra_698
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
d_LeftZero_2814 = ()
-> ()
-> T_BooleanAlgebra_698
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
forall a. a
erased
-- Algebra.Lattice.Properties.BooleanAlgebra._.RightIdentity
d_RightIdentity_2836 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_RightIdentity_2836 :: ()
-> ()
-> T_BooleanAlgebra_698
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
d_RightIdentity_2836 = ()
-> ()
-> T_BooleanAlgebra_698
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
forall a. a
erased
-- Algebra.Lattice.Properties.BooleanAlgebra._.RightInverse
d_RightInverse_2838 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny ->
  (AgdaAny -> AgdaAny) -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_RightInverse_2838 :: ()
-> ()
-> T_BooleanAlgebra_698
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
d_RightInverse_2838 = ()
-> ()
-> T_BooleanAlgebra_698
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
forall a. a
erased
-- Algebra.Lattice.Properties.BooleanAlgebra._.RightZero
d_RightZero_2844 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_RightZero_2844 :: ()
-> ()
-> T_BooleanAlgebra_698
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
d_RightZero_2844 = ()
-> ()
-> T_BooleanAlgebra_698
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
forall a. a
erased
-- Algebra.Lattice.Properties.BooleanAlgebra._.Zero
d_Zero_2864 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> ()
d_Zero_2864 :: ()
-> ()
-> T_BooleanAlgebra_698
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
d_Zero_2864 = ()
-> ()
-> T_BooleanAlgebra_698
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> ()
forall a. a
erased
-- Algebra.Lattice.Properties.BooleanAlgebra._.IsBooleanAlgebra
d_IsBooleanAlgebra_3006 :: p -> p -> p -> p -> p -> p -> p -> p -> ()
d_IsBooleanAlgebra_3006 p
a0 p
a1 p
a2 p
a3 p
a4 p
a5 p
a6 p
a7 = ()
-- Algebra.Lattice.Properties.BooleanAlgebra._.IsBooleanAlgebra.isDistributiveLattice
d_isDistributiveLattice_3034 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224 ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3146
d_isDistributiveLattice_3034 :: T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
d_isDistributiveLattice_3034 T_IsBooleanAlgebra_3224
v0
  = (T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe
      T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
      (T_IsBooleanAlgebra_3224 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0)
-- Algebra.Lattice.Properties.BooleanAlgebra._.IsBooleanAlgebra.¬-cong
d_'172''45'cong_3050 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'172''45'cong_3050 :: T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'172''45'cong_3050 T_IsBooleanAlgebra_3224
v0
  = (T_IsBooleanAlgebra_3224
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'172''45'cong_3250
      (T_IsBooleanAlgebra_3224 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0)
-- Algebra.Lattice.Properties.BooleanAlgebra._.IsBooleanAlgebra.∧-complement
d_'8743''45'complement_3058 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8743''45'complement_3058 :: T_IsBooleanAlgebra_3224 -> T_Σ_14
d_'8743''45'complement_3058 T_IsBooleanAlgebra_3224
v0
  = (T_IsBooleanAlgebra_3224 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsBooleanAlgebra_3224 -> T_Σ_14
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'complement_3248
      (T_IsBooleanAlgebra_3224 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0)
-- Algebra.Lattice.Properties.BooleanAlgebra._.IsBooleanAlgebra.∨-complement
d_'8744''45'complement_3082 ::
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8744''45'complement_3082 :: T_IsBooleanAlgebra_3224 -> T_Σ_14
d_'8744''45'complement_3082 T_IsBooleanAlgebra_3224
v0
  = (T_IsBooleanAlgebra_3224 -> T_Σ_14) -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_IsBooleanAlgebra_3224 -> T_Σ_14
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'complement_3246
      (T_IsBooleanAlgebra_3224 -> AgdaAny
forall a b. a -> b
coe T_IsBooleanAlgebra_3224
v0)
-- Algebra.Lattice.Properties.BooleanAlgebra._.poset
d_poset_3476 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Poset_492
d_poset_3476 :: () -> () -> T_BooleanAlgebra_698 -> T_Poset_492
d_poset_3476 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 = T_BooleanAlgebra_698 -> T_Poset_492
du_poset_3476 T_BooleanAlgebra_698
v2
du_poset_3476 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Relation.Binary.Bundles.T_Poset_492
du_poset_3476 :: T_BooleanAlgebra_698 -> T_Poset_492
du_poset_3476 T_BooleanAlgebra_698
v0
  = let v1 :: AgdaAny
v1
          = (T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.du_distributiveLattice_806
              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> T_Poset_492
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_DistributiveLattice_598 -> T_Lattice_512
MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_678 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Semilattice_10 -> T_Poset_492) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Semilattice_10 -> T_Poset_492
MAlonzo.Code.Algebra.Lattice.Properties.Semilattice.du_poset_162
            ((T_Lattice_512 -> T_Semilattice_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Lattice_512 -> T_Semilattice_10
MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8743''45'semilattice_306
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Lattice.Properties.BooleanAlgebra._.∧-idem
d_'8743''45'idem_3478 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny
d_'8743''45'idem_3478 :: () -> () -> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
d_'8743''45'idem_3478 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8743''45'idem_3478 T_BooleanAlgebra_698
v2
du_'8743''45'idem_3478 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny
du_'8743''45'idem_3478 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8743''45'idem_3478 T_BooleanAlgebra_698
v0
  = let v1 :: AgdaAny
v1
          = (T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.du_distributiveLattice_806
              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_Lattice_512 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Lattice_512 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8743''45'idem_294
         ((T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_Lattice_512
MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_678 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Lattice.Properties.BooleanAlgebra._.∧-isBand
d_'8743''45'isBand_3480 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
d_'8743''45'isBand_3480 :: () -> () -> T_BooleanAlgebra_698 -> T_IsBand_526
d_'8743''45'isBand_3480 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 = T_BooleanAlgebra_698 -> T_IsBand_526
du_'8743''45'isBand_3480 T_BooleanAlgebra_698
v2
du_'8743''45'isBand_3480 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
du_'8743''45'isBand_3480 :: T_BooleanAlgebra_698 -> T_IsBand_526
du_'8743''45'isBand_3480 T_BooleanAlgebra_698
v0
  = let v1 :: AgdaAny
v1
          = (T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.du_distributiveLattice_806
              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> T_IsBand_526
forall a b. a -> b
coe
      ((T_Lattice_512 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Lattice_512 -> T_IsBand_526
MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8743''45'isBand_302
         ((T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_Lattice_512
MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_678 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Lattice.Properties.BooleanAlgebra._.∧-isMagma
d_'8743''45'isMagma_3482 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_'8743''45'isMagma_3482 :: () -> () -> T_BooleanAlgebra_698 -> T_IsMagma_178
d_'8743''45'isMagma_3482 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 = T_BooleanAlgebra_698 -> T_IsMagma_178
du_'8743''45'isMagma_3482 T_BooleanAlgebra_698
v2
du_'8743''45'isMagma_3482 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
du_'8743''45'isMagma_3482 :: T_BooleanAlgebra_698 -> T_IsMagma_178
du_'8743''45'isMagma_3482 T_BooleanAlgebra_698
v0
  = let v1 :: AgdaAny
v1
          = (T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.du_distributiveLattice_806
              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      ((T_Lattice_512 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Lattice_512 -> T_IsMagma_178
MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8743''45'isMagma_298
         ((T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_Lattice_512
MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_678 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Lattice.Properties.BooleanAlgebra._.∧-isOrderTheoreticJoinSemilattice
d_'8743''45'isOrderTheoreticJoinSemilattice_3484 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Relation.Binary.Lattice.Structures.T_IsJoinSemilattice_22
d_'8743''45'isOrderTheoreticJoinSemilattice_3484 :: () -> () -> T_BooleanAlgebra_698 -> T_IsJoinSemilattice_22
d_'8743''45'isOrderTheoreticJoinSemilattice_3484 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_IsJoinSemilattice_22
du_'8743''45'isOrderTheoreticJoinSemilattice_3484 T_BooleanAlgebra_698
v2
du_'8743''45'isOrderTheoreticJoinSemilattice_3484 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Relation.Binary.Lattice.Structures.T_IsJoinSemilattice_22
du_'8743''45'isOrderTheoreticJoinSemilattice_3484 :: T_BooleanAlgebra_698 -> T_IsJoinSemilattice_22
du_'8743''45'isOrderTheoreticJoinSemilattice_3484 T_BooleanAlgebra_698
v0
  = let v1 :: AgdaAny
v1
          = (T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.du_distributiveLattice_806
              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> T_IsJoinSemilattice_22
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_DistributiveLattice_598 -> T_Lattice_512
MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_678 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Semilattice_10 -> T_IsJoinSemilattice_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Semilattice_10 -> T_IsJoinSemilattice_22
MAlonzo.Code.Algebra.Lattice.Properties.Semilattice.du_'8743''45'isOrderTheoreticJoinSemilattice_178
            ((T_Lattice_512 -> T_Semilattice_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Lattice_512 -> T_Semilattice_10
MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8743''45'semilattice_306
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Lattice.Properties.BooleanAlgebra._.∧-isOrderTheoreticMeetSemilattice
d_'8743''45'isOrderTheoreticMeetSemilattice_3486 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Relation.Binary.Lattice.Structures.T_IsMeetSemilattice_184
d_'8743''45'isOrderTheoreticMeetSemilattice_3486 :: () -> () -> T_BooleanAlgebra_698 -> T_IsMeetSemilattice_184
d_'8743''45'isOrderTheoreticMeetSemilattice_3486 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_IsMeetSemilattice_184
du_'8743''45'isOrderTheoreticMeetSemilattice_3486 T_BooleanAlgebra_698
v2
du_'8743''45'isOrderTheoreticMeetSemilattice_3486 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Relation.Binary.Lattice.Structures.T_IsMeetSemilattice_184
du_'8743''45'isOrderTheoreticMeetSemilattice_3486 :: T_BooleanAlgebra_698 -> T_IsMeetSemilattice_184
du_'8743''45'isOrderTheoreticMeetSemilattice_3486 T_BooleanAlgebra_698
v0
  = let v1 :: AgdaAny
v1
          = (T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.du_distributiveLattice_806
              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> T_IsMeetSemilattice_184
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_DistributiveLattice_598 -> T_Lattice_512
MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_678 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Semilattice_10 -> T_IsMeetSemilattice_184) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Semilattice_10 -> T_IsMeetSemilattice_184
MAlonzo.Code.Algebra.Lattice.Properties.Semilattice.du_'8743''45'isOrderTheoreticMeetSemilattice_176
            ((T_Lattice_512 -> T_Semilattice_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Lattice_512 -> T_Semilattice_10
MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8743''45'semilattice_306
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Lattice.Properties.BooleanAlgebra._.∧-isSemigroup
d_'8743''45'isSemigroup_3488 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_'8743''45'isSemigroup_3488 :: () -> () -> T_BooleanAlgebra_698 -> T_IsSemigroup_488
d_'8743''45'isSemigroup_3488 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_IsSemigroup_488
du_'8743''45'isSemigroup_3488 T_BooleanAlgebra_698
v2
du_'8743''45'isSemigroup_3488 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
du_'8743''45'isSemigroup_3488 :: T_BooleanAlgebra_698 -> T_IsSemigroup_488
du_'8743''45'isSemigroup_3488 T_BooleanAlgebra_698
v0
  = let v1 :: AgdaAny
v1
          = (T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.du_distributiveLattice_806
              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> T_IsSemigroup_488
forall a b. a -> b
coe
      ((T_Lattice_512 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Lattice_512 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8743''45'isSemigroup_300
         ((T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_Lattice_512
MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_678 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Lattice.Properties.BooleanAlgebra._.∧-isSemilattice
d_'8743''45'isSemilattice_3490 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
d_'8743''45'isSemilattice_3490 :: () -> () -> T_BooleanAlgebra_698 -> T_IsCommutativeBand_612
d_'8743''45'isSemilattice_3490 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_IsCommutativeBand_612
du_'8743''45'isSemilattice_3490 T_BooleanAlgebra_698
v2
du_'8743''45'isSemilattice_3490 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
du_'8743''45'isSemilattice_3490 :: T_BooleanAlgebra_698 -> T_IsCommutativeBand_612
du_'8743''45'isSemilattice_3490 T_BooleanAlgebra_698
v0
  = let v1 :: AgdaAny
v1
          = (T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.du_distributiveLattice_806
              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> T_IsCommutativeBand_612
forall a b. a -> b
coe
      ((T_Lattice_512 -> T_IsCommutativeBand_612) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Lattice_512 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8743''45'isSemilattice_304
         ((T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_Lattice_512
MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_678 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Lattice.Properties.BooleanAlgebra._.∧-orderTheoreticJoinSemilattice
d_'8743''45'orderTheoreticJoinSemilattice_3492 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Relation.Binary.Lattice.Bundles.T_JoinSemilattice_14
d_'8743''45'orderTheoreticJoinSemilattice_3492 :: () -> () -> T_BooleanAlgebra_698 -> T_JoinSemilattice_14
d_'8743''45'orderTheoreticJoinSemilattice_3492 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_JoinSemilattice_14
du_'8743''45'orderTheoreticJoinSemilattice_3492 T_BooleanAlgebra_698
v2
du_'8743''45'orderTheoreticJoinSemilattice_3492 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Relation.Binary.Lattice.Bundles.T_JoinSemilattice_14
du_'8743''45'orderTheoreticJoinSemilattice_3492 :: T_BooleanAlgebra_698 -> T_JoinSemilattice_14
du_'8743''45'orderTheoreticJoinSemilattice_3492 T_BooleanAlgebra_698
v0
  = let v1 :: AgdaAny
v1
          = (T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.du_distributiveLattice_806
              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> T_JoinSemilattice_14
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_DistributiveLattice_598 -> T_Lattice_512
MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_678 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Semilattice_10 -> T_JoinSemilattice_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Semilattice_10 -> T_JoinSemilattice_14
MAlonzo.Code.Algebra.Lattice.Properties.Semilattice.du_'8743''45'orderTheoreticJoinSemilattice_182
            ((T_Lattice_512 -> T_Semilattice_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Lattice_512 -> T_Semilattice_10
MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8743''45'semilattice_306
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Lattice.Properties.BooleanAlgebra._.∧-orderTheoreticMeetSemilattice
d_'8743''45'orderTheoreticMeetSemilattice_3494 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Relation.Binary.Lattice.Bundles.T_MeetSemilattice_204
d_'8743''45'orderTheoreticMeetSemilattice_3494 :: () -> () -> T_BooleanAlgebra_698 -> T_MeetSemilattice_204
d_'8743''45'orderTheoreticMeetSemilattice_3494 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_MeetSemilattice_204
du_'8743''45'orderTheoreticMeetSemilattice_3494 T_BooleanAlgebra_698
v2
du_'8743''45'orderTheoreticMeetSemilattice_3494 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Relation.Binary.Lattice.Bundles.T_MeetSemilattice_204
du_'8743''45'orderTheoreticMeetSemilattice_3494 :: T_BooleanAlgebra_698 -> T_MeetSemilattice_204
du_'8743''45'orderTheoreticMeetSemilattice_3494 T_BooleanAlgebra_698
v0
  = let v1 :: AgdaAny
v1
          = (T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.du_distributiveLattice_806
              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> T_MeetSemilattice_204
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_DistributiveLattice_598 -> T_Lattice_512
MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_678 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Semilattice_10 -> T_MeetSemilattice_204) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Semilattice_10 -> T_MeetSemilattice_204
MAlonzo.Code.Algebra.Lattice.Properties.Semilattice.du_'8743''45'orderTheoreticMeetSemilattice_180
            ((T_Lattice_512 -> T_Semilattice_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Lattice_512 -> T_Semilattice_10
MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8743''45'semilattice_306
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Lattice.Properties.BooleanAlgebra._.∧-semilattice
d_'8743''45'semilattice_3496 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_Semilattice_10
d_'8743''45'semilattice_3496 :: () -> () -> T_BooleanAlgebra_698 -> T_Semilattice_10
d_'8743''45'semilattice_3496 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_Semilattice_10
du_'8743''45'semilattice_3496 T_BooleanAlgebra_698
v2
du_'8743''45'semilattice_3496 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_Semilattice_10
du_'8743''45'semilattice_3496 :: T_BooleanAlgebra_698 -> T_Semilattice_10
du_'8743''45'semilattice_3496 T_BooleanAlgebra_698
v0
  = let v1 :: AgdaAny
v1
          = (T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.du_distributiveLattice_806
              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> T_Semilattice_10
forall a b. a -> b
coe
      ((T_Lattice_512 -> T_Semilattice_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Lattice_512 -> T_Semilattice_10
MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8743''45'semilattice_306
         ((T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_Lattice_512
MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_678 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Lattice.Properties.BooleanAlgebra._.∧-∨-distributiveLattice
d_'8743''45''8744''45'distributiveLattice_3498 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_598
d_'8743''45''8744''45'distributiveLattice_3498 :: () -> () -> T_BooleanAlgebra_698 -> T_DistributiveLattice_598
d_'8743''45''8744''45'distributiveLattice_3498 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_DistributiveLattice_598
du_'8743''45''8744''45'distributiveLattice_3498 T_BooleanAlgebra_698
v2
du_'8743''45''8744''45'distributiveLattice_3498 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_DistributiveLattice_598
du_'8743''45''8744''45'distributiveLattice_3498 :: T_BooleanAlgebra_698 -> T_DistributiveLattice_598
du_'8743''45''8744''45'distributiveLattice_3498 T_BooleanAlgebra_698
v0
  = (T_DistributiveLattice_598 -> T_DistributiveLattice_598)
-> AgdaAny -> T_DistributiveLattice_598
forall a b. a -> b
coe
      T_DistributiveLattice_598 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Properties.DistributiveLattice.du_'8743''45''8744''45'distributiveLattice_744
      ((T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_BooleanAlgebra_698 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.du_distributiveLattice_806
         (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
-- Algebra.Lattice.Properties.BooleanAlgebra._.∧-∨-isDistributiveLattice
d_'8743''45''8744''45'isDistributiveLattice_3500 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3146
d_'8743''45''8744''45'isDistributiveLattice_3500 :: () -> () -> T_BooleanAlgebra_698 -> T_IsDistributiveLattice_3146
d_'8743''45''8744''45'isDistributiveLattice_3500 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_IsDistributiveLattice_3146
du_'8743''45''8744''45'isDistributiveLattice_3500 T_BooleanAlgebra_698
v2
du_'8743''45''8744''45'isDistributiveLattice_3500 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsDistributiveLattice_3146
du_'8743''45''8744''45'isDistributiveLattice_3500 :: T_BooleanAlgebra_698 -> T_IsDistributiveLattice_3146
du_'8743''45''8744''45'isDistributiveLattice_3500 T_BooleanAlgebra_698
v0
  = (T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe
      T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Properties.DistributiveLattice.du_'8743''45''8744''45'isDistributiveLattice_742
      ((T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_BooleanAlgebra_698 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.du_distributiveLattice_806
         (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
-- Algebra.Lattice.Properties.BooleanAlgebra._.∧-∨-isLattice
d_'8743''45''8744''45'isLattice_3502 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_3070
d_'8743''45''8744''45'isLattice_3502 :: () -> () -> T_BooleanAlgebra_698 -> T_IsLattice_3070
d_'8743''45''8744''45'isLattice_3502 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_IsLattice_3070
du_'8743''45''8744''45'isLattice_3502 T_BooleanAlgebra_698
v2
du_'8743''45''8744''45'isLattice_3502 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsLattice_3070
du_'8743''45''8744''45'isLattice_3502 :: T_BooleanAlgebra_698 -> T_IsLattice_3070
du_'8743''45''8744''45'isLattice_3502 T_BooleanAlgebra_698
v0
  = let v1 :: AgdaAny
v1
          = (T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.du_distributiveLattice_806
              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> T_IsLattice_3070
forall a b. a -> b
coe
      ((T_Lattice_512 -> T_IsLattice_3070) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Lattice_512 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8743''45''8744''45'isLattice_342
         ((T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_Lattice_512
MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_678 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Lattice.Properties.BooleanAlgebra._.∧-∨-lattice
d_'8743''45''8744''45'lattice_3504 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_512
d_'8743''45''8744''45'lattice_3504 :: () -> () -> T_BooleanAlgebra_698 -> T_Lattice_512
d_'8743''45''8744''45'lattice_3504 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_Lattice_512
du_'8743''45''8744''45'lattice_3504 T_BooleanAlgebra_698
v2
du_'8743''45''8744''45'lattice_3504 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_Lattice_512
du_'8743''45''8744''45'lattice_3504 :: T_BooleanAlgebra_698 -> T_Lattice_512
du_'8743''45''8744''45'lattice_3504 T_BooleanAlgebra_698
v0
  = let v1 :: AgdaAny
v1
          = (T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.du_distributiveLattice_806
              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> T_Lattice_512
forall a b. a -> b
coe
      ((T_Lattice_512 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Lattice_512 -> T_Lattice_512
MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8743''45''8744''45'lattice_344
         ((T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_Lattice_512
MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_678 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Lattice.Properties.BooleanAlgebra._.∨-idem
d_'8744''45'idem_3506 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny
d_'8744''45'idem_3506 :: () -> () -> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
d_'8744''45'idem_3506 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8744''45'idem_3506 T_BooleanAlgebra_698
v2
du_'8744''45'idem_3506 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny
du_'8744''45'idem_3506 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8744''45'idem_3506 T_BooleanAlgebra_698
v0
  = let v1 :: AgdaAny
v1
          = (T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.du_distributiveLattice_806
              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      ((T_Lattice_512 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Lattice_512 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8744''45'idem_318
         ((T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_Lattice_512
MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_678 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Lattice.Properties.BooleanAlgebra._.∨-isBand
d_'8744''45'isBand_3508 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
d_'8744''45'isBand_3508 :: () -> () -> T_BooleanAlgebra_698 -> T_IsBand_526
d_'8744''45'isBand_3508 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 = T_BooleanAlgebra_698 -> T_IsBand_526
du_'8744''45'isBand_3508 T_BooleanAlgebra_698
v2
du_'8744''45'isBand_3508 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsBand_526
du_'8744''45'isBand_3508 :: T_BooleanAlgebra_698 -> T_IsBand_526
du_'8744''45'isBand_3508 T_BooleanAlgebra_698
v0
  = let v1 :: AgdaAny
v1
          = (T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.du_distributiveLattice_806
              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> T_IsBand_526
forall a b. a -> b
coe
      ((T_Lattice_512 -> T_IsBand_526) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Lattice_512 -> T_IsBand_526
MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8744''45'isBand_326
         ((T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_Lattice_512
MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_678 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Lattice.Properties.BooleanAlgebra._.∨-isMagma
d_'8744''45'isMagma_3510 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_'8744''45'isMagma_3510 :: () -> () -> T_BooleanAlgebra_698 -> T_IsMagma_178
d_'8744''45'isMagma_3510 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 = T_BooleanAlgebra_698 -> T_IsMagma_178
du_'8744''45'isMagma_3510 T_BooleanAlgebra_698
v2
du_'8744''45'isMagma_3510 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
du_'8744''45'isMagma_3510 :: T_BooleanAlgebra_698 -> T_IsMagma_178
du_'8744''45'isMagma_3510 T_BooleanAlgebra_698
v0
  = let v1 :: AgdaAny
v1
          = (T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.du_distributiveLattice_806
              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      ((T_Lattice_512 -> T_IsMagma_178) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Lattice_512 -> T_IsMagma_178
MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8744''45'isMagma_322
         ((T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_Lattice_512
MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_678 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Lattice.Properties.BooleanAlgebra._.∧-isOrderTheoreticJoinSemilattice
d_'8743''45'isOrderTheoreticJoinSemilattice_3512 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Relation.Binary.Lattice.Structures.T_IsJoinSemilattice_22
d_'8743''45'isOrderTheoreticJoinSemilattice_3512 :: () -> () -> T_BooleanAlgebra_698 -> T_IsJoinSemilattice_22
d_'8743''45'isOrderTheoreticJoinSemilattice_3512 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_IsJoinSemilattice_22
du_'8743''45'isOrderTheoreticJoinSemilattice_3512 T_BooleanAlgebra_698
v2
du_'8743''45'isOrderTheoreticJoinSemilattice_3512 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Relation.Binary.Lattice.Structures.T_IsJoinSemilattice_22
du_'8743''45'isOrderTheoreticJoinSemilattice_3512 :: T_BooleanAlgebra_698 -> T_IsJoinSemilattice_22
du_'8743''45'isOrderTheoreticJoinSemilattice_3512 T_BooleanAlgebra_698
v0
  = let v1 :: AgdaAny
v1
          = (T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.du_distributiveLattice_806
              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> T_IsJoinSemilattice_22
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_DistributiveLattice_598 -> T_Lattice_512
MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_678 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Semilattice_10 -> T_IsJoinSemilattice_22) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Semilattice_10 -> T_IsJoinSemilattice_22
MAlonzo.Code.Algebra.Lattice.Properties.Semilattice.du_'8743''45'isOrderTheoreticJoinSemilattice_178
            ((T_Lattice_512 -> T_Semilattice_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Lattice_512 -> T_Semilattice_10
MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8744''45'semilattice_330
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Lattice.Properties.BooleanAlgebra._.∧-isOrderTheoreticMeetSemilattice
d_'8743''45'isOrderTheoreticMeetSemilattice_3514 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Relation.Binary.Lattice.Structures.T_IsMeetSemilattice_184
d_'8743''45'isOrderTheoreticMeetSemilattice_3514 :: () -> () -> T_BooleanAlgebra_698 -> T_IsMeetSemilattice_184
d_'8743''45'isOrderTheoreticMeetSemilattice_3514 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_IsMeetSemilattice_184
du_'8743''45'isOrderTheoreticMeetSemilattice_3514 T_BooleanAlgebra_698
v2
du_'8743''45'isOrderTheoreticMeetSemilattice_3514 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Relation.Binary.Lattice.Structures.T_IsMeetSemilattice_184
du_'8743''45'isOrderTheoreticMeetSemilattice_3514 :: T_BooleanAlgebra_698 -> T_IsMeetSemilattice_184
du_'8743''45'isOrderTheoreticMeetSemilattice_3514 T_BooleanAlgebra_698
v0
  = let v1 :: AgdaAny
v1
          = (T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.du_distributiveLattice_806
              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> T_IsMeetSemilattice_184
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_DistributiveLattice_598 -> T_Lattice_512
MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_678 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Semilattice_10 -> T_IsMeetSemilattice_184) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Semilattice_10 -> T_IsMeetSemilattice_184
MAlonzo.Code.Algebra.Lattice.Properties.Semilattice.du_'8743''45'isOrderTheoreticMeetSemilattice_176
            ((T_Lattice_512 -> T_Semilattice_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Lattice_512 -> T_Semilattice_10
MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8744''45'semilattice_330
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Lattice.Properties.BooleanAlgebra._.∨-isSemigroup
d_'8744''45'isSemigroup_3516 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_'8744''45'isSemigroup_3516 :: () -> () -> T_BooleanAlgebra_698 -> T_IsSemigroup_488
d_'8744''45'isSemigroup_3516 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_IsSemigroup_488
du_'8744''45'isSemigroup_3516 T_BooleanAlgebra_698
v2
du_'8744''45'isSemigroup_3516 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
du_'8744''45'isSemigroup_3516 :: T_BooleanAlgebra_698 -> T_IsSemigroup_488
du_'8744''45'isSemigroup_3516 T_BooleanAlgebra_698
v0
  = let v1 :: AgdaAny
v1
          = (T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.du_distributiveLattice_806
              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> T_IsSemigroup_488
forall a b. a -> b
coe
      ((T_Lattice_512 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Lattice_512 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8744''45'isSemigroup_324
         ((T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_Lattice_512
MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_678 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Lattice.Properties.BooleanAlgebra._.∨-isSemilattice
d_'8744''45'isSemilattice_3518 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
d_'8744''45'isSemilattice_3518 :: () -> () -> T_BooleanAlgebra_698 -> T_IsCommutativeBand_612
d_'8744''45'isSemilattice_3518 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_IsCommutativeBand_612
du_'8744''45'isSemilattice_3518 T_BooleanAlgebra_698
v2
du_'8744''45'isSemilattice_3518 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeBand_612
du_'8744''45'isSemilattice_3518 :: T_BooleanAlgebra_698 -> T_IsCommutativeBand_612
du_'8744''45'isSemilattice_3518 T_BooleanAlgebra_698
v0
  = let v1 :: AgdaAny
v1
          = (T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.du_distributiveLattice_806
              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> T_IsCommutativeBand_612
forall a b. a -> b
coe
      ((T_Lattice_512 -> T_IsCommutativeBand_612) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Lattice_512 -> T_IsCommutativeBand_612
MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8744''45'isSemilattice_328
         ((T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_Lattice_512
MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_678 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Lattice.Properties.BooleanAlgebra._.∧-orderTheoreticJoinSemilattice
d_'8743''45'orderTheoreticJoinSemilattice_3520 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Relation.Binary.Lattice.Bundles.T_JoinSemilattice_14
d_'8743''45'orderTheoreticJoinSemilattice_3520 :: () -> () -> T_BooleanAlgebra_698 -> T_JoinSemilattice_14
d_'8743''45'orderTheoreticJoinSemilattice_3520 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_JoinSemilattice_14
du_'8743''45'orderTheoreticJoinSemilattice_3520 T_BooleanAlgebra_698
v2
du_'8743''45'orderTheoreticJoinSemilattice_3520 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Relation.Binary.Lattice.Bundles.T_JoinSemilattice_14
du_'8743''45'orderTheoreticJoinSemilattice_3520 :: T_BooleanAlgebra_698 -> T_JoinSemilattice_14
du_'8743''45'orderTheoreticJoinSemilattice_3520 T_BooleanAlgebra_698
v0
  = let v1 :: AgdaAny
v1
          = (T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.du_distributiveLattice_806
              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> T_JoinSemilattice_14
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_DistributiveLattice_598 -> T_Lattice_512
MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_678 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Semilattice_10 -> T_JoinSemilattice_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Semilattice_10 -> T_JoinSemilattice_14
MAlonzo.Code.Algebra.Lattice.Properties.Semilattice.du_'8743''45'orderTheoreticJoinSemilattice_182
            ((T_Lattice_512 -> T_Semilattice_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Lattice_512 -> T_Semilattice_10
MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8744''45'semilattice_330
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Lattice.Properties.BooleanAlgebra._.∧-orderTheoreticMeetSemilattice
d_'8743''45'orderTheoreticMeetSemilattice_3522 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Relation.Binary.Lattice.Bundles.T_MeetSemilattice_204
d_'8743''45'orderTheoreticMeetSemilattice_3522 :: () -> () -> T_BooleanAlgebra_698 -> T_MeetSemilattice_204
d_'8743''45'orderTheoreticMeetSemilattice_3522 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_MeetSemilattice_204
du_'8743''45'orderTheoreticMeetSemilattice_3522 T_BooleanAlgebra_698
v2
du_'8743''45'orderTheoreticMeetSemilattice_3522 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Relation.Binary.Lattice.Bundles.T_MeetSemilattice_204
du_'8743''45'orderTheoreticMeetSemilattice_3522 :: T_BooleanAlgebra_698 -> T_MeetSemilattice_204
du_'8743''45'orderTheoreticMeetSemilattice_3522 T_BooleanAlgebra_698
v0
  = let v1 :: AgdaAny
v1
          = (T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.du_distributiveLattice_806
              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> T_MeetSemilattice_204
forall a b. a -> b
coe
      (let v2 :: AgdaAny
v2
             = (T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_DistributiveLattice_598 -> T_Lattice_512
MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_678 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) in
       AgdaAny -> AgdaAny
forall a b. a -> b
coe
         ((T_Semilattice_10 -> T_MeetSemilattice_204) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_Semilattice_10 -> T_MeetSemilattice_204
MAlonzo.Code.Algebra.Lattice.Properties.Semilattice.du_'8743''45'orderTheoreticMeetSemilattice_180
            ((T_Lattice_512 -> T_Semilattice_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Lattice_512 -> T_Semilattice_10
MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8744''45'semilattice_330
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Lattice.Properties.BooleanAlgebra._.∨-semilattice
d_'8744''45'semilattice_3524 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_Semilattice_10
d_'8744''45'semilattice_3524 :: () -> () -> T_BooleanAlgebra_698 -> T_Semilattice_10
d_'8744''45'semilattice_3524 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_Semilattice_10
du_'8744''45'semilattice_3524 T_BooleanAlgebra_698
v2
du_'8744''45'semilattice_3524 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_Semilattice_10
du_'8744''45'semilattice_3524 :: T_BooleanAlgebra_698 -> T_Semilattice_10
du_'8744''45'semilattice_3524 T_BooleanAlgebra_698
v0
  = let v1 :: AgdaAny
v1
          = (T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.du_distributiveLattice_806
              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> T_Semilattice_10
forall a b. a -> b
coe
      ((T_Lattice_512 -> T_Semilattice_10) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Lattice_512 -> T_Semilattice_10
MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8744''45'semilattice_330
         ((T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_Lattice_512
MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_678 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Lattice.Properties.BooleanAlgebra._.∨-∧-isOrderTheoreticLattice
d_'8744''45''8743''45'isOrderTheoreticLattice_3526 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Relation.Binary.Lattice.Structures.T_IsLattice_348
d_'8744''45''8743''45'isOrderTheoreticLattice_3526 :: () -> () -> T_BooleanAlgebra_698 -> T_IsLattice_348
d_'8744''45''8743''45'isOrderTheoreticLattice_3526 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_IsLattice_348
du_'8744''45''8743''45'isOrderTheoreticLattice_3526 T_BooleanAlgebra_698
v2
du_'8744''45''8743''45'isOrderTheoreticLattice_3526 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Relation.Binary.Lattice.Structures.T_IsLattice_348
du_'8744''45''8743''45'isOrderTheoreticLattice_3526 :: T_BooleanAlgebra_698 -> T_IsLattice_348
du_'8744''45''8743''45'isOrderTheoreticLattice_3526 T_BooleanAlgebra_698
v0
  = let v1 :: AgdaAny
v1
          = (T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.du_distributiveLattice_806
              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> T_IsLattice_348
forall a b. a -> b
coe
      ((T_Lattice_512 -> T_IsLattice_348) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Lattice_512 -> T_IsLattice_348
MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8744''45''8743''45'isOrderTheoreticLattice_356
         ((T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_Lattice_512
MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_678 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Lattice.Properties.BooleanAlgebra._.∨-∧-orderTheoreticLattice
d_'8744''45''8743''45'orderTheoreticLattice_3528 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Relation.Binary.Lattice.Bundles.T_Lattice_394
d_'8744''45''8743''45'orderTheoreticLattice_3528 :: () -> () -> T_BooleanAlgebra_698 -> T_Lattice_394
d_'8744''45''8743''45'orderTheoreticLattice_3528 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_Lattice_394
du_'8744''45''8743''45'orderTheoreticLattice_3528 T_BooleanAlgebra_698
v2
du_'8744''45''8743''45'orderTheoreticLattice_3528 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Relation.Binary.Lattice.Bundles.T_Lattice_394
du_'8744''45''8743''45'orderTheoreticLattice_3528 :: T_BooleanAlgebra_698 -> T_Lattice_394
du_'8744''45''8743''45'orderTheoreticLattice_3528 T_BooleanAlgebra_698
v0
  = let v1 :: AgdaAny
v1
          = (T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.du_distributiveLattice_806
              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) in
    AgdaAny -> T_Lattice_394
forall a b. a -> b
coe
      ((T_Lattice_512 -> T_Lattice_394) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Lattice_512 -> T_Lattice_394
MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8744''45''8743''45'orderTheoreticLattice_412
         ((T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_DistributiveLattice_598 -> T_Lattice_512
MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_678 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)))
-- Algebra.Lattice.Properties.BooleanAlgebra.∧-∨-isBooleanAlgebra
d_'8743''45''8744''45'isBooleanAlgebra_3530 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224
d_'8743''45''8744''45'isBooleanAlgebra_3530 :: () -> () -> T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
d_'8743''45''8744''45'isBooleanAlgebra_3530 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
du_'8743''45''8744''45'isBooleanAlgebra_3530 T_BooleanAlgebra_698
v2
du_'8743''45''8744''45'isBooleanAlgebra_3530 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Lattice.Structures.T_IsBooleanAlgebra_3224
du_'8743''45''8744''45'isBooleanAlgebra_3530 :: T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
du_'8743''45''8744''45'isBooleanAlgebra_3530 T_BooleanAlgebra_698
v0
  = (T_IsDistributiveLattice_3146
 -> T_Σ_14
 -> T_Σ_14
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsBooleanAlgebra_3224)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_3224
forall a b. a -> b
coe
      T_IsDistributiveLattice_3146
-> T_Σ_14
-> T_Σ_14
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Structures.C_constructor_3314
      ((T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_DistributiveLattice_598 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Properties.DistributiveLattice.du_'8743''45''8744''45'isDistributiveLattice_742
         ((T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.du_distributiveLattice_806
            (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
      ((T_IsBooleanAlgebra_3224 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBooleanAlgebra_3224 -> T_Σ_14
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'complement_3248
         ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
            (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
      ((T_IsBooleanAlgebra_3224 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBooleanAlgebra_3224 -> T_Σ_14
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'complement_3246
         ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
            (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
      ((T_IsBooleanAlgebra_3224
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'172''45'cong_3250
         ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
            (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
-- Algebra.Lattice.Properties.BooleanAlgebra.∧-∨-booleanAlgebra
d_'8743''45''8744''45'booleanAlgebra_3532 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698
d_'8743''45''8744''45'booleanAlgebra_3532 :: () -> () -> T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
d_'8743''45''8744''45'booleanAlgebra_3532 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
du_'8743''45''8744''45'booleanAlgebra_3532 T_BooleanAlgebra_698
v2
du_'8743''45''8744''45'booleanAlgebra_3532 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698
du_'8743''45''8744''45'booleanAlgebra_3532 :: T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
du_'8743''45''8744''45'booleanAlgebra_3532 T_BooleanAlgebra_698
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> T_IsBooleanAlgebra_3224
 -> T_BooleanAlgebra_698)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_BooleanAlgebra_698
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsBooleanAlgebra_3224
-> T_BooleanAlgebra_698
MAlonzo.Code.Algebra.Lattice.Bundles.C_constructor_822
      (T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      (T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      (T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
du_'8743''45''8744''45'isBooleanAlgebra_3530 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
-- Algebra.Lattice.Properties.BooleanAlgebra.∧-identityʳ
d_'8743''45'identity'691'_3534 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny
d_'8743''45'identity'691'_3534 :: () -> () -> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
d_'8743''45'identity'691'_3534 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 AgdaAny
v3
  = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8743''45'identity'691'_3534 T_BooleanAlgebra_698
v2 AgdaAny
v3
du_'8743''45'identity'691'_3534 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny
du_'8743''45'identity'691'_3534 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8743''45'identity'691'_3534 T_BooleanAlgebra_698
v0 AgdaAny
v1
  = ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
      (\ AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 ->
         (T__IsRelatedTo__26 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T__IsRelatedTo__26 -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 AgdaAny
v4)
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
         (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
      AgdaAny
v1
      (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
            ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                  ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
            (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1)))
         AgdaAny
v1
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
               ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                  ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                     ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                        ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                           ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1)))
            AgdaAny
v1 AgdaAny
v1
            (((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_494
               (((AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                  ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                     ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                        ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                           ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                              ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1))
            ((T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'absorbs'45''8744'_3122
               (T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                  ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe
                     T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                     ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                        (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
               AgdaAny
v1 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1)))
         ((T_IsLattice_3070
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'cong'737'_3124
            ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
               ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                  ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                     (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)
            ((T_BooleanAlgebra_698 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1))
            ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
               (T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                  ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> T_IsLattice_3070
forall a b. a -> b
coe
                     T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1))
               (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
               ((T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny)
-> T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'complement'691'_3308
                  (T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                     (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
                  AgdaAny
v1))))
-- Algebra.Lattice.Properties.BooleanAlgebra.∧-identityˡ
d_'8743''45'identity'737'_3538 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny
d_'8743''45'identity'737'_3538 :: () -> () -> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
d_'8743''45'identity'737'_3538 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8743''45'identity'737'_3538 T_BooleanAlgebra_698
v2
du_'8743''45'identity'737'_3538 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny
du_'8743''45'identity'737'_3538 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8743''45'identity'737'_3538 T_BooleanAlgebra_698
v0
  = (T_Setoid_46
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_Setoid_46
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Setoid.du_comm'8743'id'691''8658'id'737'_366
      ((T_Lattice_512 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Lattice_512 -> T_Setoid_46
MAlonzo.Code.Algebra.Lattice.Bundles.du_setoid_586
         ((T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_DistributiveLattice_598 -> T_Lattice_512
MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_678
            ((T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.du_distributiveLattice_806
               (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      ((T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'comm_3100
         ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
            ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
               ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                  (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
      ((T_BooleanAlgebra_698 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8743''45'identity'691'_3534 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
-- Algebra.Lattice.Properties.BooleanAlgebra.∧-identity
d_'8743''45'identity_3540 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8743''45'identity_3540 :: () -> () -> T_BooleanAlgebra_698 -> T_Σ_14
d_'8743''45'identity_3540 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_Σ_14
du_'8743''45'identity_3540 T_BooleanAlgebra_698
v2
du_'8743''45'identity_3540 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8743''45'identity_3540 :: T_BooleanAlgebra_698 -> T_Σ_14
du_'8743''45'identity_3540 T_BooleanAlgebra_698
v0
  = (AgdaAny -> AgdaAny -> T_Σ_14) -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      AgdaAny -> AgdaAny -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8743''45'identity'737'_3538 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8743''45'identity'691'_3534 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
-- Algebra.Lattice.Properties.BooleanAlgebra.∨-identityʳ
d_'8744''45'identity'691'_3542 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny
d_'8744''45'identity'691'_3542 :: () -> () -> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
d_'8744''45'identity'691'_3542 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 AgdaAny
v3
  = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8744''45'identity'691'_3542 T_BooleanAlgebra_698
v2 AgdaAny
v3
du_'8744''45'identity'691'_3542 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny
du_'8744''45'identity'691'_3542 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8744''45'identity'691'_3542 T_BooleanAlgebra_698
v0 AgdaAny
v1
  = ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
      (\ AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 ->
         (T__IsRelatedTo__26 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T__IsRelatedTo__26 -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 AgdaAny
v4)
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1
         (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
      AgdaAny
v1
      (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
            ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                  ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1
            (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1)))
         AgdaAny
v1
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
               ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                  ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                     ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                        ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                           ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1)))
            AgdaAny
v1 AgdaAny
v1
            (((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_494
               (((AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                  ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                     ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                        ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                           ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                              ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1))
            ((T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'absorbs'45''8743'_3120
               (T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                  ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe
                     T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                     ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                        (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
               AgdaAny
v1 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1)))
         ((T_IsLattice_3070
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'cong'737'_3132
            ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
               ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                  ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                     (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)
            ((T_BooleanAlgebra_698 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1))
            ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
               (T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                  ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> T_IsLattice_3070
forall a b. a -> b
coe
                     T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1))
               (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
               ((T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny)
-> T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'complement'691'_3312
                  (T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                     (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
                  AgdaAny
v1))))
-- Algebra.Lattice.Properties.BooleanAlgebra.∨-identityˡ
d_'8744''45'identity'737'_3546 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny
d_'8744''45'identity'737'_3546 :: () -> () -> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
d_'8744''45'identity'737'_3546 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8744''45'identity'737'_3546 T_BooleanAlgebra_698
v2
du_'8744''45'identity'737'_3546 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny
du_'8744''45'identity'737'_3546 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8744''45'identity'737'_3546 T_BooleanAlgebra_698
v0
  = (T_Setoid_46
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_Setoid_46
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Setoid.du_comm'8743'id'691''8658'id'737'_366
      ((T_Lattice_512 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Lattice_512 -> T_Setoid_46
MAlonzo.Code.Algebra.Lattice.Bundles.du_setoid_586
         ((T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_DistributiveLattice_598 -> T_Lattice_512
MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_678
            ((T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.du_distributiveLattice_806
               (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      ((T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'comm_3094
         ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
            ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
               ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                  (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
      ((T_BooleanAlgebra_698 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8744''45'identity'691'_3542 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
-- Algebra.Lattice.Properties.BooleanAlgebra.∨-identity
d_'8744''45'identity_3548 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8744''45'identity_3548 :: () -> () -> T_BooleanAlgebra_698 -> T_Σ_14
d_'8744''45'identity_3548 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_Σ_14
du_'8744''45'identity_3548 T_BooleanAlgebra_698
v2
du_'8744''45'identity_3548 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8744''45'identity_3548 :: T_BooleanAlgebra_698 -> T_Σ_14
du_'8744''45'identity_3548 T_BooleanAlgebra_698
v0
  = (AgdaAny -> AgdaAny -> T_Σ_14) -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      AgdaAny -> AgdaAny -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8744''45'identity'737'_3546 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8744''45'identity'691'_3542 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
-- Algebra.Lattice.Properties.BooleanAlgebra.∧-zeroʳ
d_'8743''45'zero'691'_3550 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny
d_'8743''45'zero'691'_3550 :: () -> () -> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
d_'8743''45'zero'691'_3550 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 AgdaAny
v3
  = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8743''45'zero'691'_3550 T_BooleanAlgebra_698
v2 AgdaAny
v3
du_'8743''45'zero'691'_3550 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny
du_'8743''45'zero'691'_3550 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8743''45'zero'691'_3550 T_BooleanAlgebra_698
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
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v3 AgdaAny
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 AgdaAny
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_372
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
            ((T_IsEquivalence_28
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                  ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
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forall a b. a -> b
coe
                     T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
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forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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         (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
            ((T_IsLattice_3070 -> T_IsEquivalence_28)
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forall a b. a -> b
coe
               T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
               ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
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forall a b. a -> b
coe
                  T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                  ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
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forall a b. a -> b
coe
                     T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
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forall a b. a -> b
coe
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MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_372
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                  ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                     ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
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forall a b. a -> b
coe
                        T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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forall a b. a -> b
coe
                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
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forall a b. a -> b
coe
                              T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
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coe
                  T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                  ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
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forall a b. a -> b
coe
                     T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
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forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
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coe
                        T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
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                           T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
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coe
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MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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                        (AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                        ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                           ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                              ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                                 ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                    T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                    ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                       T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                       (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
                     ((T_BooleanAlgebra_698 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
                  ((T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny)
-> T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'complement'691'_3312
                     (T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                        (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
                     AgdaAny
v1))
               ((T_IsLattice_3070
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'cong'691'_3128
                  ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1)
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v1)
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)
                  ((T_Lattice_512 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_Lattice_512 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8743''45'idem_294
                     ((T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_DistributiveLattice_598 -> T_Lattice_512
MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_678
                        ((T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.du_distributiveLattice_806
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1))))
            ((T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'assoc_3102
               (T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                  ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe
                     T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                     ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                        (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
               AgdaAny
v1 AgdaAny
v1
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1)))
         ((T_IsLattice_3070
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'cong'737'_3124
            ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
               ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                  ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                     (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1))
            ((T_BooleanAlgebra_698 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
            ((T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny)
-> T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'complement'691'_3312
               (T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                  (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
               AgdaAny
v1)))
-- Algebra.Lattice.Properties.BooleanAlgebra.∧-zeroˡ
d_'8743''45'zero'737'_3554 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny
d_'8743''45'zero'737'_3554 :: () -> () -> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
d_'8743''45'zero'737'_3554 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8743''45'zero'737'_3554 T_BooleanAlgebra_698
v2
du_'8743''45'zero'737'_3554 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny
du_'8743''45'zero'737'_3554 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8743''45'zero'737'_3554 T_BooleanAlgebra_698
v0
  = (T_Setoid_46
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_Setoid_46
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Setoid.du_comm'8743'ze'691''8658'ze'737'_386
      ((T_Lattice_512 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Lattice_512 -> T_Setoid_46
MAlonzo.Code.Algebra.Lattice.Bundles.du_setoid_586
         ((T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_DistributiveLattice_598 -> T_Lattice_512
MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_678
            ((T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.du_distributiveLattice_806
               (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      ((T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'comm_3100
         ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
            ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
               ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                  (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
      ((T_BooleanAlgebra_698 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8743''45'zero'691'_3550 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
-- Algebra.Lattice.Properties.BooleanAlgebra.∧-zero
d_'8743''45'zero_3556 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8743''45'zero_3556 :: () -> () -> T_BooleanAlgebra_698 -> T_Σ_14
d_'8743''45'zero_3556 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 = T_BooleanAlgebra_698 -> T_Σ_14
du_'8743''45'zero_3556 T_BooleanAlgebra_698
v2
du_'8743''45'zero_3556 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8743''45'zero_3556 :: T_BooleanAlgebra_698 -> T_Σ_14
du_'8743''45'zero_3556 T_BooleanAlgebra_698
v0
  = (AgdaAny -> AgdaAny -> T_Σ_14) -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      AgdaAny -> AgdaAny -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8743''45'zero'737'_3554 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8743''45'zero'691'_3550 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
-- Algebra.Lattice.Properties.BooleanAlgebra.∨-zeroʳ
d_'8744''45'zero'691'_3560 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny
d_'8744''45'zero'691'_3560 :: () -> () -> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
d_'8744''45'zero'691'_3560 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 AgdaAny
v3
  = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8744''45'zero'691'_3560 T_BooleanAlgebra_698
v2 AgdaAny
v3
du_'8744''45'zero'691'_3560 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny
du_'8744''45'zero'691'_3560 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8744''45'zero'691'_3560 T_BooleanAlgebra_698
v0 AgdaAny
v1
  = ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
      (\ AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 ->
         (T__IsRelatedTo__26 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T__IsRelatedTo__26 -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 AgdaAny
v4)
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1
         (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
      (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_372
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
            ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                  ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
         (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
            ((T_IsLattice_3070 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
               T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
               ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                  ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                     ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                        (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))))
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1
            (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1
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-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1
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coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1)))
         (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_372
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
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 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
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coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
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-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
               ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                  ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                     ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                        ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                           ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
               ((T_IsLattice_3070 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
                  T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                  ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1
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-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
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coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
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v1)))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
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-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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v1 AgdaAny
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1))
            (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
               (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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coe
                  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                  ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                     ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                        ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                           ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                              ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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forall a b. a -> b
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                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
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coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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v1 AgdaAny
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                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
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               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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forall a b. a -> b
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                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
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               (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
               (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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coe
                  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
                  (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
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coe
                     (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                     ((T_IsEquivalence_28
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-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                        ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                           ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                              ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
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forall a b. a -> b
coe
                                 T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                 ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                    T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                    (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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forall a b. a -> b
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                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
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                  (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
                  (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
                  (((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny)
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forall a b. a -> b
coe
                     (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_494
                     (((AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                        ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                           ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                              ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                                 ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                    T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                    ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
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forall a b. a -> b
coe
                                       T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                       (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
                     ((T_BooleanAlgebra_698 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny
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coe T_BooleanAlgebra_698
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                  ((T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny)
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forall a b. a -> b
coe
                     T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'complement'691'_3308
                     (T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                        (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
                     AgdaAny
v1))
               ((T_IsLattice_3070
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-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLattice_3070
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MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'cong'691'_3136
                  ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
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forall a b. a -> b
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                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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v1 AgdaAny
v1)
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)
                  ((T_Lattice_512 -> AgdaAny -> AgdaAny)
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forall a b. a -> b
coe
                     T_Lattice_512 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8744''45'idem_318
                     ((T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_DistributiveLattice_598 -> T_Lattice_512
MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_678
                        ((T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.du_distributiveLattice_806
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1))))
            ((T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'assoc_3096
               (T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                  ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe
                     T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                     ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                        (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
               AgdaAny
v1 AgdaAny
v1
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1)))
         ((T_IsLattice_3070
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'cong'737'_3132
            ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
               ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                  ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                     (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1))
            ((T_BooleanAlgebra_698 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
            ((T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny)
-> T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'complement'691'_3308
               (T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                  (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
               AgdaAny
v1)))
-- Algebra.Lattice.Properties.BooleanAlgebra.∨-zeroˡ
d_'8744''45'zero'737'_3564 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny
d_'8744''45'zero'737'_3564 :: () -> () -> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
d_'8744''45'zero'737'_3564 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8744''45'zero'737'_3564 T_BooleanAlgebra_698
v2
du_'8744''45'zero'737'_3564 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny
du_'8744''45'zero'737'_3564 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8744''45'zero'737'_3564 T_BooleanAlgebra_698
v0
  = (T_Setoid_46
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_Setoid_46
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Setoid.du_comm'8743'ze'691''8658'ze'737'_386
      ((T_Lattice_512 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Lattice_512 -> T_Setoid_46
MAlonzo.Code.Algebra.Lattice.Bundles.du_setoid_586
         ((T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_DistributiveLattice_598 -> T_Lattice_512
MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_678
            ((T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.du_distributiveLattice_806
               (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      ((T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'comm_3094
         ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
            ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
               ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                  (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
      ((T_BooleanAlgebra_698 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8744''45'zero'691'_3560 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
-- Algebra.Lattice.Properties.BooleanAlgebra.∨-zero
d_'8744''45'zero_3566 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8744''45'zero_3566 :: () -> () -> T_BooleanAlgebra_698 -> T_Σ_14
d_'8744''45'zero_3566 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 = T_BooleanAlgebra_698 -> T_Σ_14
du_'8744''45'zero_3566 T_BooleanAlgebra_698
v2
du_'8744''45'zero_3566 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8744''45'zero_3566 :: T_BooleanAlgebra_698 -> T_Σ_14
du_'8744''45'zero_3566 T_BooleanAlgebra_698
v0
  = (AgdaAny -> AgdaAny -> T_Σ_14) -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      AgdaAny -> AgdaAny -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8744''45'zero'737'_3564 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8744''45'zero'691'_3560 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
-- Algebra.Lattice.Properties.BooleanAlgebra.∨-⊥-isMonoid
d_'8744''45''8869''45'isMonoid_3568 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_'8744''45''8869''45'isMonoid_3568 :: () -> () -> T_BooleanAlgebra_698 -> T_IsMonoid_712
d_'8744''45''8869''45'isMonoid_3568 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_IsMonoid_712
du_'8744''45''8869''45'isMonoid_3568 T_BooleanAlgebra_698
v2
du_'8744''45''8869''45'isMonoid_3568 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
du_'8744''45''8869''45'isMonoid_3568 :: T_BooleanAlgebra_698 -> T_IsMonoid_712
du_'8744''45''8869''45'isMonoid_3568 T_BooleanAlgebra_698
v0
  = (T_IsSemigroup_488 -> T_Σ_14 -> T_IsMonoid_712)
-> AgdaAny -> AgdaAny -> T_IsMonoid_712
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_Σ_14 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.C_constructor_758
      ((T_Lattice_512 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Lattice_512 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8744''45'isSemigroup_324
         ((T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_DistributiveLattice_598 -> T_Lattice_512
MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_678
            ((T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.du_distributiveLattice_806
               (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
      ((T_BooleanAlgebra_698 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_Σ_14
du_'8744''45'identity_3548 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
-- Algebra.Lattice.Properties.BooleanAlgebra.∧-⊤-isMonoid
d_'8743''45''8868''45'isMonoid_3570 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_'8743''45''8868''45'isMonoid_3570 :: () -> () -> T_BooleanAlgebra_698 -> T_IsMonoid_712
d_'8743''45''8868''45'isMonoid_3570 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_IsMonoid_712
du_'8743''45''8868''45'isMonoid_3570 T_BooleanAlgebra_698
v2
du_'8743''45''8868''45'isMonoid_3570 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
du_'8743''45''8868''45'isMonoid_3570 :: T_BooleanAlgebra_698 -> T_IsMonoid_712
du_'8743''45''8868''45'isMonoid_3570 T_BooleanAlgebra_698
v0
  = (T_IsSemigroup_488 -> T_Σ_14 -> T_IsMonoid_712)
-> AgdaAny -> AgdaAny -> T_IsMonoid_712
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_Σ_14 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.C_constructor_758
      ((T_Lattice_512 -> T_IsSemigroup_488) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Lattice_512 -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8743''45'isSemigroup_300
         ((T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_DistributiveLattice_598 -> T_Lattice_512
MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_678
            ((T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.du_distributiveLattice_806
               (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
      ((T_BooleanAlgebra_698 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_Σ_14
du_'8743''45'identity_3540 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
-- Algebra.Lattice.Properties.BooleanAlgebra.∨-⊥-isCommutativeMonoid
d_'8744''45''8869''45'isCommutativeMonoid_3572 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764
d_'8744''45''8869''45'isCommutativeMonoid_3572 :: () -> () -> T_BooleanAlgebra_698 -> T_IsCommutativeMonoid_764
d_'8744''45''8869''45'isCommutativeMonoid_3572 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_IsCommutativeMonoid_764
du_'8744''45''8869''45'isCommutativeMonoid_3572 T_BooleanAlgebra_698
v2
du_'8744''45''8869''45'isCommutativeMonoid_3572 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764
du_'8744''45''8869''45'isCommutativeMonoid_3572 :: T_BooleanAlgebra_698 -> T_IsCommutativeMonoid_764
du_'8744''45''8869''45'isCommutativeMonoid_3572 T_BooleanAlgebra_698
v0
  = (T_IsMonoid_712
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe
      T_IsMonoid_712
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.C_constructor_820
      ((T_BooleanAlgebra_698 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_IsMonoid_712
du_'8744''45''8869''45'isMonoid_3568 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      ((T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'comm_3094
         ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
            ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
               ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                  (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
-- Algebra.Lattice.Properties.BooleanAlgebra.∧-⊤-isCommutativeMonoid
d_'8743''45''8868''45'isCommutativeMonoid_3574 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764
d_'8743''45''8868''45'isCommutativeMonoid_3574 :: () -> () -> T_BooleanAlgebra_698 -> T_IsCommutativeMonoid_764
d_'8743''45''8868''45'isCommutativeMonoid_3574 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_IsCommutativeMonoid_764
du_'8743''45''8868''45'isCommutativeMonoid_3574 T_BooleanAlgebra_698
v2
du_'8743''45''8868''45'isCommutativeMonoid_3574 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeMonoid_764
du_'8743''45''8868''45'isCommutativeMonoid_3574 :: T_BooleanAlgebra_698 -> T_IsCommutativeMonoid_764
du_'8743''45''8868''45'isCommutativeMonoid_3574 T_BooleanAlgebra_698
v0
  = (T_IsMonoid_712
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny -> T_IsCommutativeMonoid_764
forall a b. a -> b
coe
      T_IsMonoid_712
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeMonoid_764
MAlonzo.Code.Algebra.Structures.C_constructor_820
      ((T_BooleanAlgebra_698 -> T_IsMonoid_712) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_IsMonoid_712
du_'8743''45''8868''45'isMonoid_3570 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      ((T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'comm_3100
         ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
            ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
               ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                  (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
-- Algebra.Lattice.Properties.BooleanAlgebra.∨-∧-isSemiring
d_'8744''45''8743''45'isSemiring_3576 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640
d_'8744''45''8743''45'isSemiring_3576 :: () -> () -> T_BooleanAlgebra_698 -> T_IsSemiring_1640
d_'8744''45''8743''45'isSemiring_3576 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_IsSemiring_1640
du_'8744''45''8743''45'isSemiring_3576 T_BooleanAlgebra_698
v2
du_'8744''45''8743''45'isSemiring_3576 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640
du_'8744''45''8743''45'isSemiring_3576 :: T_BooleanAlgebra_698 -> T_IsSemiring_1640
du_'8744''45''8743''45'isSemiring_3576 T_BooleanAlgebra_698
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_Σ_14 -> T_IsSemiring_1640)
-> AgdaAny -> AgdaAny -> T_IsSemiring_1640
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1536
-> T_Σ_14 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.C_constructor_1740
      ((T_IsCommutativeMonoid_764
 -> (AgdaAny
     -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_Σ_14
 -> T_Σ_14
 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764
-> (AgdaAny
    -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_Σ_14
-> T_Σ_14
-> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.C_constructor_1630
         ((T_BooleanAlgebra_698 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_IsCommutativeMonoid_764
du_'8744''45''8869''45'isCommutativeMonoid_3572 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
         ((T_IsLattice_3070
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_3070
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'cong_3104
            ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
               ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                  ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                     (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
         ((T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'assoc_3102
            ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
               ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                  ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                     (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
         ((T_BooleanAlgebra_698 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_Σ_14
du_'8743''45'identity_3540 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
         ((T_IsDistributiveLattice_3146 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3146 -> T_Σ_14
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'distrib'45''8744'_3162
            ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
               ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                  (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
      ((T_BooleanAlgebra_698 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_Σ_14
du_'8743''45'zero_3556 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
-- Algebra.Lattice.Properties.BooleanAlgebra.∧-∨-isSemiring
d_'8743''45''8744''45'isSemiring_3578 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640
d_'8743''45''8744''45'isSemiring_3578 :: () -> () -> T_BooleanAlgebra_698 -> T_IsSemiring_1640
d_'8743''45''8744''45'isSemiring_3578 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_IsSemiring_1640
du_'8743''45''8744''45'isSemiring_3578 T_BooleanAlgebra_698
v2
du_'8743''45''8744''45'isSemiring_3578 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemiring_1640
du_'8743''45''8744''45'isSemiring_3578 :: T_BooleanAlgebra_698 -> T_IsSemiring_1640
du_'8743''45''8744''45'isSemiring_3578 T_BooleanAlgebra_698
v0
  = (T_IsSemiringWithoutAnnihilatingZero_1536
 -> T_Σ_14 -> T_IsSemiring_1640)
-> AgdaAny -> AgdaAny -> T_IsSemiring_1640
forall a b. a -> b
coe
      T_IsSemiringWithoutAnnihilatingZero_1536
-> T_Σ_14 -> T_IsSemiring_1640
MAlonzo.Code.Algebra.Structures.C_constructor_1740
      ((T_IsCommutativeMonoid_764
 -> (AgdaAny
     -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_Σ_14
 -> T_Σ_14
 -> T_IsSemiringWithoutAnnihilatingZero_1536)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsCommutativeMonoid_764
-> (AgdaAny
    -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_Σ_14
-> T_Σ_14
-> T_IsSemiringWithoutAnnihilatingZero_1536
MAlonzo.Code.Algebra.Structures.C_constructor_1630
         ((T_BooleanAlgebra_698 -> T_IsCommutativeMonoid_764)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_IsCommutativeMonoid_764
du_'8743''45''8868''45'isCommutativeMonoid_3574 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
         ((T_IsLattice_3070
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_3070
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'cong_3098
            ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
               ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                  ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                     (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
         ((T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'assoc_3096
            ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
               ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                  ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                     (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
         ((T_BooleanAlgebra_698 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_Σ_14
du_'8744''45'identity_3548 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
         ((T_IsDistributiveLattice_3146 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3146 -> T_Σ_14
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'distrib'45''8743'_3160
            ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
               ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                  (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
      ((T_BooleanAlgebra_698 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_Σ_14
du_'8744''45'zero_3566 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
-- Algebra.Lattice.Properties.BooleanAlgebra.∨-∧-isCommutativeSemiring
d_'8744''45''8743''45'isCommutativeSemiring_3580 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750
d_'8744''45''8743''45'isCommutativeSemiring_3580 :: () -> () -> T_BooleanAlgebra_698 -> T_IsCommutativeSemiring_1750
d_'8744''45''8743''45'isCommutativeSemiring_3580 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_IsCommutativeSemiring_1750
du_'8744''45''8743''45'isCommutativeSemiring_3580 T_BooleanAlgebra_698
v2
du_'8744''45''8743''45'isCommutativeSemiring_3580 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750
du_'8744''45''8743''45'isCommutativeSemiring_3580 :: T_BooleanAlgebra_698 -> T_IsCommutativeSemiring_1750
du_'8744''45''8743''45'isCommutativeSemiring_3580 T_BooleanAlgebra_698
v0
  = (T_IsSemiring_1640
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeSemiring_1750)
-> AgdaAny -> AgdaAny -> T_IsCommutativeSemiring_1750
forall a b. a -> b
coe
      T_IsSemiring_1640
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeSemiring_1750
MAlonzo.Code.Algebra.Structures.C_constructor_1862
      ((T_BooleanAlgebra_698 -> T_IsSemiring_1640) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_IsSemiring_1640
du_'8744''45''8743''45'isSemiring_3576 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      ((T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'comm_3100
         ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
            ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
               ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                  (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
-- Algebra.Lattice.Properties.BooleanAlgebra.∧-∨-isCommutativeSemiring
d_'8743''45''8744''45'isCommutativeSemiring_3582 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750
d_'8743''45''8744''45'isCommutativeSemiring_3582 :: () -> () -> T_BooleanAlgebra_698 -> T_IsCommutativeSemiring_1750
d_'8743''45''8744''45'isCommutativeSemiring_3582 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_IsCommutativeSemiring_1750
du_'8743''45''8744''45'isCommutativeSemiring_3582 T_BooleanAlgebra_698
v2
du_'8743''45''8744''45'isCommutativeSemiring_3582 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeSemiring_1750
du_'8743''45''8744''45'isCommutativeSemiring_3582 :: T_BooleanAlgebra_698 -> T_IsCommutativeSemiring_1750
du_'8743''45''8744''45'isCommutativeSemiring_3582 T_BooleanAlgebra_698
v0
  = (T_IsSemiring_1640
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeSemiring_1750)
-> AgdaAny -> AgdaAny -> T_IsCommutativeSemiring_1750
forall a b. a -> b
coe
      T_IsSemiring_1640
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeSemiring_1750
MAlonzo.Code.Algebra.Structures.C_constructor_1862
      ((T_BooleanAlgebra_698 -> T_IsSemiring_1640) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_IsSemiring_1640
du_'8743''45''8744''45'isSemiring_3578 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      ((T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'comm_3094
         ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
            ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
               ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                  (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
-- Algebra.Lattice.Properties.BooleanAlgebra.∨-∧-commutativeSemiring
d_'8744''45''8743''45'commutativeSemiring_3584 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Bundles.T_CommutativeSemiring_2524
d_'8744''45''8743''45'commutativeSemiring_3584 :: () -> () -> T_BooleanAlgebra_698 -> T_CommutativeSemiring_2524
d_'8744''45''8743''45'commutativeSemiring_3584 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_CommutativeSemiring_2524
du_'8744''45''8743''45'commutativeSemiring_3584 T_BooleanAlgebra_698
v2
du_'8744''45''8743''45'commutativeSemiring_3584 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Bundles.T_CommutativeSemiring_2524
du_'8744''45''8743''45'commutativeSemiring_3584 :: T_BooleanAlgebra_698 -> T_CommutativeSemiring_2524
du_'8744''45''8743''45'commutativeSemiring_3584 T_BooleanAlgebra_698
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> T_IsCommutativeSemiring_1750
 -> T_CommutativeSemiring_2524)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_CommutativeSemiring_2524
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1750
-> T_CommutativeSemiring_2524
MAlonzo.Code.Algebra.Bundles.C_constructor_2706
      (T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      (T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      ((T_BooleanAlgebra_698 -> T_IsCommutativeSemiring_1750)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_IsCommutativeSemiring_1750
du_'8744''45''8743''45'isCommutativeSemiring_3580 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
-- Algebra.Lattice.Properties.BooleanAlgebra.∧-∨-commutativeSemiring
d_'8743''45''8744''45'commutativeSemiring_3586 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Bundles.T_CommutativeSemiring_2524
d_'8743''45''8744''45'commutativeSemiring_3586 :: () -> () -> T_BooleanAlgebra_698 -> T_CommutativeSemiring_2524
d_'8743''45''8744''45'commutativeSemiring_3586 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_CommutativeSemiring_2524
du_'8743''45''8744''45'commutativeSemiring_3586 T_BooleanAlgebra_698
v2
du_'8743''45''8744''45'commutativeSemiring_3586 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Bundles.T_CommutativeSemiring_2524
du_'8743''45''8744''45'commutativeSemiring_3586 :: T_BooleanAlgebra_698 -> T_CommutativeSemiring_2524
du_'8743''45''8744''45'commutativeSemiring_3586 T_BooleanAlgebra_698
v0
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> T_IsCommutativeSemiring_1750
 -> T_CommutativeSemiring_2524)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_CommutativeSemiring_2524
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeSemiring_1750
-> T_CommutativeSemiring_2524
MAlonzo.Code.Algebra.Bundles.C_constructor_2706
      (T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      (T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      ((T_BooleanAlgebra_698 -> T_IsCommutativeSemiring_1750)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_IsCommutativeSemiring_1750
du_'8743''45''8744''45'isCommutativeSemiring_3582 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
-- Algebra.Lattice.Properties.BooleanAlgebra.lemma
d_lemma_3592 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_lemma_3592 :: ()
-> ()
-> T_BooleanAlgebra_698
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_lemma_3592 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 = T_BooleanAlgebra_698
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_lemma_3592 T_BooleanAlgebra_698
v2 AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 AgdaAny
v6
du_lemma_3592 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_lemma_3592 :: T_BooleanAlgebra_698
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_lemma_3592 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4
  = ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
      (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
         (T__IsRelatedTo__26 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T__IsRelatedTo__26 -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 AgdaAny
v7)
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1) AgdaAny
v2
      (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_372
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
            ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                  ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
         (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
            ((T_IsLattice_3070 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
               T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
               ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                  ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                     ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                        (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))))
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1)
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1)
            (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
         AgdaAny
v2
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_372
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
               ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                  ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                     ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                        ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                           ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
               ((T_IsLattice_3070 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
                  T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                  ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1)
               (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2))
            AgdaAny
v2
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
               (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                  ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                     ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                        ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                           ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                              ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1)
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2))
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1) AgdaAny
v1)
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1) AgdaAny
v2))
               AgdaAny
v2
               (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
                  (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
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                        T_IsEquivalence_28
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
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forall a b. a -> b
coe
                           T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                           ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                              ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
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forall a b. a -> b
coe
                                 T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                 ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
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forall a b. a -> b
coe
                                    T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_372
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                        ((T_IsEquivalence_28
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coe
                           T_IsEquivalence_28
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                           ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                              ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                                 ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
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forall a b. a -> b
coe
                                    T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                    ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
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forall a b. a -> b
coe
                                       T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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                     (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
                        ((T_IsLattice_3070 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
                           T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                           ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
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forall a b. a -> b
coe
                              T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                              ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
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forall a b. a -> b
coe
                                 T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                 ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
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forall a b. a -> b
coe
                                    T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                    (T_BooleanAlgebra_698 -> AgdaAny
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                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
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                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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                           T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_372
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                           ((T_IsEquivalence_28
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forall a b. a -> b
coe
                              T_IsEquivalence_28
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                              ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                                 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                    T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                                    ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
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forall a b. a -> b
coe
                                       T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                       ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
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forall a b. a -> b
coe
                                          T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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                        (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
                           ((T_IsLattice_3070 -> T_IsEquivalence_28)
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forall a b. a -> b
coe
                              T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                              ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
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forall a b. a -> b
coe
                                 T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                                 ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
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forall a b. a -> b
coe
                                    T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                    ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
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forall a b. a -> b
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                                       T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
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coe
                                    T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
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forall a b. a -> b
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                                       T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
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MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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forall a b. a -> b
coe
                              (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
                              (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                                 ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                    T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                                    ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                       T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                                       ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                          T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                                          ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                             T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                             ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                                T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                                (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
                              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                                 (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)) AgdaAny
v2)
                              AgdaAny
v2 AgdaAny
v2
                              (((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_494
                                 (((AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                    (AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                                    ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                       T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                                       ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                          T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                                          ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                             T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                                             ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                                T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                                ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                                   T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                                   (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
                                 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))
                              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8743''45'identity'737'_3538 T_BooleanAlgebra_698
v0 AgdaAny
v2))
                           ((T_IsLattice_3070
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'cong'691'_3128
                              ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                                 ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                    T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                    ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                       T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                       (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
                              (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)
                              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1
                                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1))
                              ((T_BooleanAlgebra_698 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
                              ((T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny)
-> T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'complement'691'_3308
                                 (T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                    (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
                                 AgdaAny
v1)))
                        ((T_IsDistributiveLattice_3146
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_3146
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                           T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'distrib'691''45''8744'_3210
                           (T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                              ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> T_IsBooleanAlgebra_3224
forall a b. a -> b
coe
                                 T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
                           AgdaAny
v2 AgdaAny
v1
                           ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1)))
                     ((T_IsLattice_3070
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'cong'691'_3136
                        ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                           ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                              ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
                        ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                           ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1) AgdaAny
v2)
                        ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
                        ((T_BooleanAlgebra_698 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
                        (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))
                  ((T_IsLattice_3070
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'cong'691'_3136
                     ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                        ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                           ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                        ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1) AgdaAny
v2)
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                        ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1) AgdaAny
v1)
                     ((T_BooleanAlgebra_698 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
                     ((T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny)
-> T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'complement'737'_3310
                        (T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
                        AgdaAny
v1)))
               ((T_IsDistributiveLattice_3146
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_3146
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                  T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'distrib'737''45''8744'_3208
                  (T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                     ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> T_IsBooleanAlgebra_3224
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                        (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1) AgdaAny
v1
                  AgdaAny
v2))
            ((T_IsLattice_3070
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'cong'737'_3124
               ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                  ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                     ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                        (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
               ((T_BooleanAlgebra_698 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4)))
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8743''45'identity'691'_3534 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1)))
-- Algebra.Lattice.Properties.BooleanAlgebra.¬⊥≈⊤
d_'172''8869''8776''8868'_3602 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny
d_'172''8869''8776''8868'_3602 :: () -> () -> T_BooleanAlgebra_698 -> AgdaAny
d_'172''8869''8776''8868'_3602 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> AgdaAny
du_'172''8869''8776''8868'_3602 T_BooleanAlgebra_698
v2
du_'172''8869''8776''8868'_3602 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny
du_'172''8869''8776''8868'_3602 :: T_BooleanAlgebra_698 -> AgdaAny
du_'172''8869''8776''8868'_3602 T_BooleanAlgebra_698
v0
  = (T_BooleanAlgebra_698
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_BooleanAlgebra_698
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_lemma_3592 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
      ((T_BooleanAlgebra_698 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      ((T_BooleanAlgebra_698 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8743''45'identity'691'_3534 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
         ((T_BooleanAlgebra_698 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8744''45'zero'691'_3560 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
         ((T_BooleanAlgebra_698 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
-- Algebra.Lattice.Properties.BooleanAlgebra.¬⊤≈⊥
d_'172''8868''8776''8869'_3604 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny
d_'172''8868''8776''8869'_3604 :: () -> () -> T_BooleanAlgebra_698 -> AgdaAny
d_'172''8868''8776''8869'_3604 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> AgdaAny
du_'172''8868''8776''8869'_3604 T_BooleanAlgebra_698
v2
du_'172''8868''8776''8869'_3604 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny
du_'172''8868''8776''8869'_3604 :: T_BooleanAlgebra_698 -> AgdaAny
du_'172''8868''8776''8869'_3604 T_BooleanAlgebra_698
v0
  = (T_BooleanAlgebra_698
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_BooleanAlgebra_698
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_lemma_3592 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
      ((T_BooleanAlgebra_698 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      ((T_BooleanAlgebra_698 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8743''45'zero'691'_3550 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
         ((T_BooleanAlgebra_698 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8744''45'identity'691'_3542 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
         ((T_BooleanAlgebra_698 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
-- Algebra.Lattice.Properties.BooleanAlgebra.¬-involutive
d_'172''45'involutive_3606 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny
d_'172''45'involutive_3606 :: () -> () -> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
d_'172''45'involutive_3606 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 AgdaAny
v3
  = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'172''45'involutive_3606 T_BooleanAlgebra_698
v2 AgdaAny
v3
du_'172''45'involutive_3606 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny
du_'172''45'involutive_3606 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'172''45'involutive_3606 T_BooleanAlgebra_698
v0 AgdaAny
v1
  = (T_BooleanAlgebra_698
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_BooleanAlgebra_698
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_lemma_3592 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1)
      (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)
      ((T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny)
-> T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'complement'737'_3310
         (T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
            (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
         AgdaAny
v1)
      ((T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny)
-> T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'complement'737'_3306
         (T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
            (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
         AgdaAny
v1)
-- Algebra.Lattice.Properties.BooleanAlgebra.deMorgan₁
d_deMorgan'8321'_3614 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_deMorgan'8321'_3614 :: () -> () -> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
d_deMorgan'8321'_3614 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 AgdaAny
v3 AgdaAny
v4
  = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
du_deMorgan'8321'_3614 T_BooleanAlgebra_698
v2 AgdaAny
v3 AgdaAny
v4
du_deMorgan'8321'_3614 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny
du_deMorgan'8321'_3614 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
du_deMorgan'8321'_3614 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2
  = (T_BooleanAlgebra_698
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_BooleanAlgebra_698
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_lemma_3592 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1)
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2))
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
du_lem'8321'_3624 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
du_lem'8322'_3628 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))
-- Algebra.Lattice.Properties.BooleanAlgebra._.lem₁
d_lem'8321'_3624 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_lem'8321'_3624 :: () -> () -> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
d_lem'8321'_3624 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 AgdaAny
v3 AgdaAny
v4 = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
du_lem'8321'_3624 T_BooleanAlgebra_698
v2 AgdaAny
v3 AgdaAny
v4
du_lem'8321'_3624 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny
du_lem'8321'_3624 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
du_lem'8321'_3624 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2
  = ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
      (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
         (T__IsRelatedTo__26 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T__IsRelatedTo__26 -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 AgdaAny
v5)
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1)
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2)))
      (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
            ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                  ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2)))
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2)))
         (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
               ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                  ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                     ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                        ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                           ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                              (T_BooleanAlgebra_698 -> AgdaAny
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coe T_BooleanAlgebra_698
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            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
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coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
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coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
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coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
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            (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
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coe T_BooleanAlgebra_698
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            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
               (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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                  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                  ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                     ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                        ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                           ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                              ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
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                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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v2
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                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
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                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
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               (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
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               (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
                  (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                     ((T_IsEquivalence_28
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                        T_IsEquivalence_28
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                        ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                           ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
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forall a b. a -> b
coe
                              T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                              ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
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forall a b. a -> b
coe
                                 T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                 ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
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forall a b. a -> b
coe
                                    T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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                  (T_BooleanAlgebra_698 -> AgdaAny
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                           ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                              ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
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forall a b. a -> b
coe
                                 T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                                 ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
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forall a b. a -> b
coe
                                    T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                    ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
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                                       T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                       (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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forall a b. a -> b
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                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
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-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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coe
                           T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v2
                           (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
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                           T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
                           (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
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                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                        (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
                        (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
                     (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
                     (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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                        (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
                        (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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forall a b. a -> b
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                           (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                           ((T_IsEquivalence_28
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-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                              ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                                 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                    T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                                    ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                       T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                       ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                          T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                          (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
                        ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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                           T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                           (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
                           (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
                        (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
                        (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
                        (((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny)
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forall a b. a -> b
coe
                           (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_494
                           (((AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              (AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                              ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                                 ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                    T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                                    ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                       T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                                       ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                          T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                          ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                             T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                             (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
                           ((T_BooleanAlgebra_698 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
                        ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8744''45'identity'691'_3542 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
                           ((T_BooleanAlgebra_698 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
                     ((AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Base.du__'10216'_'10217'__240
                        ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
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forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8743''45'zero'691'_3550 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
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MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'cong_3098
                           (T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                              ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe
                                 T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                 ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
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forall a b. a -> b
coe
                                    T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                    (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
                           ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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forall a b. a -> b
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                              T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v2
                              (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
                           (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
                           ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
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                              T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
                              (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
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                           (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
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                        ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
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forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8743''45'zero'691'_3550 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) (AgdaAny -> AgdaAny
forall a b. a -> b
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v1))))
                  ((AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny)
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forall a b. a -> b
coe
                     AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Base.du__'10216'_'10217'__240
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-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsLattice_3070
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MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'cong'737'_3124
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forall a b. a -> b
coe
                           T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                           ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                              ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
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forall a b. a -> b
coe
                                 T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
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                           T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> AgdaAny
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forall a b. a -> b
coe
                           T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'complement'691'_3312
                           (T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                              (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'cong_3098
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MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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forall a b. a -> b
coe
                              T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                              ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
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forall a b. a -> b
coe
                                 T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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MAlonzo.Code.Function.Base.du__'45''10216'_'8739'_292
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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                           (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
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MAlonzo.Code.Function.Base.du__'45''10216'_'8739'_292
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'complement'691'_3312
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MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'assoc_3102
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-> T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'comm_3100
                     (T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                        ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe
                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                           ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
                     AgdaAny
v1 AgdaAny
v2))))
         ((T_IsDistributiveLattice_3146
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-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3146
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MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'distrib'737''45''8744'_3208
            (T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
               ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> T_IsBooleanAlgebra_3224
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                  (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
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coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2)))
-- Algebra.Lattice.Properties.BooleanAlgebra._.lem₃
d_lem'8323'_3626 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_lem'8323'_3626 :: () -> () -> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
d_lem'8323'_3626 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 AgdaAny
v3 AgdaAny
v4 = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
du_lem'8323'_3626 T_BooleanAlgebra_698
v2 AgdaAny
v3 AgdaAny
v4
du_lem'8323'_3626 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny
du_lem'8323'_3626 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
du_lem'8323'_3626 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2
  = ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
      (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
         (T__IsRelatedTo__26 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T__IsRelatedTo__26 -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 AgdaAny
v5)
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
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         T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
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-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
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-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
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-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
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v2)
      (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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-> AgdaAny
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coe
         (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
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 -> T__IsRelatedTo__26
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-> AgdaAny -> AgdaAny
forall a b. a -> b
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            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
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-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
            ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                  ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
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-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
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            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
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-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
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            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
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-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1
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-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
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            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v2
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-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
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coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
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         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1) AgdaAny
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         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
               ((T_IsEquivalence_28
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-> AgdaAny -> AgdaAny
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                  T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                  ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                     ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                        ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                           ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
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                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
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                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
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               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                  ((T_IsEquivalence_28
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-> AgdaAny -> AgdaAny
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                     ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                        ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                           ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
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forall a b. a -> b
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                              T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                              ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
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forall a b. a -> b
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MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                 (T_BooleanAlgebra_698 -> AgdaAny
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v2
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1))
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1) AgdaAny
v2)
               (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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-> AgdaAny
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-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
                  (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
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-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                     ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                        ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                           ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                              ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                 ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                    T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                    (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v2
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1))
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1) AgdaAny
v2)
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1) AgdaAny
v2)
                  (((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_494
                     (((AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                        ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                           ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                              ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                                 ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                    T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                    ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                       T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                       (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                        ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1) AgdaAny
v2))
                  ((T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'comm_3094
                     (T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                        ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe
                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                           ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
                     AgdaAny
v2 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
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coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1)))
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8743''45'identity'737'_3538 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v2
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1))))
            ((T_IsLattice_3070
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'cong'691'_3128
               ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                  ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                     ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                        (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v2
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
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coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1))
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1))
               ((T_BooleanAlgebra_698 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
               ((T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny)
-> T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'complement'691'_3308
                  (T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                     (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
                  AgdaAny
v1)))
         ((T_IsDistributiveLattice_3146
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_3146
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'distrib'691''45''8743'_3206
            (T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
               ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> T_IsBooleanAlgebra_3224
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                  (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1) AgdaAny
v1
            AgdaAny
v2))
-- Algebra.Lattice.Properties.BooleanAlgebra._.lem₂
d_lem'8322'_3628 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_lem'8322'_3628 :: () -> () -> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
d_lem'8322'_3628 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 AgdaAny
v3 AgdaAny
v4 = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
du_lem'8322'_3628 T_BooleanAlgebra_698
v2 AgdaAny
v3 AgdaAny
v4
du_lem'8322'_3628 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny
du_lem'8322'_3628 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
du_lem'8322'_3628 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2
  = ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
      (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
         (T__IsRelatedTo__26 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T__IsRelatedTo__26 -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 AgdaAny
v5)
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
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         T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1)
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2)))
      (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
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-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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-> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
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-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_372
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
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-> T__IsRelatedTo__26
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
            ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                  ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
         (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
            ((T_IsLattice_3070 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
               T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
               ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                  ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                     ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                        (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
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v0))))))
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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v0
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coe T_BooleanAlgebra_698
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         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
               ((T_IsEquivalence_28
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-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                  ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                     ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                        ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                           ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                              (T_BooleanAlgebra_698 -> AgdaAny
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               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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v0
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                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
               (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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                  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                  ((T_IsEquivalence_28
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-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                     ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                        ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                           ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                              ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
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forall a b. a -> b
coe
                                 T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                 (T_BooleanAlgebra_698 -> AgdaAny
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v0)))))))
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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v0
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                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                        ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
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forall a b. a -> b
coe
                              T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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                                 T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
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                                    T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
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forall a b. a -> b
coe
                              T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                              ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
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forall a b. a -> b
coe
                                 T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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forall a b. a -> b
coe
                                    T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                    ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
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forall a b. a -> b
coe
                                       T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                       (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
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                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
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                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
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                     (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
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                     (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
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                     (((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
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                        (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_494
                        (((AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           (AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                           ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                              ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                                 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                    T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                                    ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                       T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                       ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                          T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                          (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
                        ((T_BooleanAlgebra_698 -> AgdaAny) -> AgdaAny -> AgdaAny
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coe T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> AgdaAny
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                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
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                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8744''45'zero'691'_3560 (T_BooleanAlgebra_698 -> AgdaAny
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
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                  ((T_IsLattice_3070
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'cong'737'_3132
                     ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                        ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                           ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
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                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
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                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v2
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
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                     ((T_BooleanAlgebra_698 -> AgdaAny) -> AgdaAny -> AgdaAny
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
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                     ((T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny)
-> T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'complement'691'_3308
                        (T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
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coe T_BooleanAlgebra_698
v0))
                        AgdaAny
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               ((T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
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coe
                  T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'assoc_3096
                  (T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
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coe T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1) AgdaAny
v2
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
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            ((T_IsLattice_3070
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-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'cong'691'_3136
               ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                  ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                     ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
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forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                        (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
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                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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v1 AgdaAny
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
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                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
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-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1) AgdaAny
v2)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
du_lem'8323'_3626 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
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         ((T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
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            T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'assoc_3096
            (T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
               ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe
                  T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                  ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                     (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
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            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
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            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
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coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
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-- Algebra.Lattice.Properties.BooleanAlgebra.deMorgan₂
d_deMorgan'8322'_3634 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_deMorgan'8322'_3634 :: () -> () -> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
d_deMorgan'8322'_3634 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 AgdaAny
v3 AgdaAny
v4
  = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
du_deMorgan'8322'_3634 T_BooleanAlgebra_698
v2 AgdaAny
v3 AgdaAny
v4
du_deMorgan'8322'_3634 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny
du_deMorgan'8322'_3634 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
du_deMorgan'8322'_3634 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2
  = ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
      (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
         (T__IsRelatedTo__26 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 AgdaAny
v5)
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
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forall a b. a -> b
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         T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
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-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2))
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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         T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
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      (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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         (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_372
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
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            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
            ((T_IsEquivalence_28
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-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                  ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
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         (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
            ((T_IsLattice_3070 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
               T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
               ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                  ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                     ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                        (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
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         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
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                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1)
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2)))
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1))
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2)))
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
du_deMorgan'8321'_3614 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1)
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2))))
         ((T_IsBooleanAlgebra_3224
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsBooleanAlgebra_3224
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
            T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'172''45'cong_3250
            (T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
               (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1))
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2)))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
            ((AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Base.du__'10216'_'10217'__240
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'172''45'involutive_3606 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1))
               ((T_IsLattice_3070
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> T_IsLattice_3070
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                  T_IsLattice_3070
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'cong_3098
                  (T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1))
                  AgdaAny
v1
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2))
                  AgdaAny
v2)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'172''45'involutive_3606 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)))))
-- Algebra.Lattice.Properties.BooleanAlgebra.XorRing._⊕_
d__'8853'__3650 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
d__'8853'__3650 :: T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
d__'8853'__3650 ~T_BooleanAlgebra_698
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 ~AgdaAny -> AgdaAny -> AgdaAny
v2 = (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'8853'__3650 AgdaAny -> AgdaAny -> AgdaAny
v1
du__'8853'__3650 ::
  (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'8853'__3650 :: (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du__'8853'__3650 AgdaAny -> AgdaAny -> AgdaAny
v0 = (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v0
-- Algebra.Lattice.Properties.BooleanAlgebra.XorRing.helper
d_helper_3660 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_helper_3660 :: ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_helper_3660 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 ~AgdaAny -> AgdaAny -> AgdaAny
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
  = T_BooleanAlgebra_698
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_helper_3660 T_BooleanAlgebra_698
v2 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
du_helper_3660 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_helper_3660 :: T_BooleanAlgebra_698
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_helper_3660 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 AgdaAny
v6
  = (AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Base.du__'10216'_'10217'__240 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v5)
      ((T_IsLattice_3070
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> T_IsLattice_3070
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_3070
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'cong_3104
         (T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
            ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe
               T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
               ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                  (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
         AgdaAny
v1 AgdaAny
v2
         (((AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Base.du__'45''10216'_'8739'_292
            (T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
            (\ AgdaAny
v7 AgdaAny
v8 -> AgdaAny
v7) AgdaAny
v3 AgdaAny
v4)
         (((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__298
            (\ AgdaAny
v7 AgdaAny
v8 -> AgdaAny
v8)
            (T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)) AgdaAny
v3
            AgdaAny
v4))
      ((T_IsBooleanAlgebra_3224
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsBooleanAlgebra_3224
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
         T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'172''45'cong_3250
         (T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
            (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
         AgdaAny
v3 AgdaAny
v4 AgdaAny
v6)
-- Algebra.Lattice.Properties.BooleanAlgebra.XorRing.⊕-cong
d_'8853''45'cong_3666 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8853''45'cong_3666 :: ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8853''45'cong_3666 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
  = T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8853''45'cong_3666 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 AgdaAny
v9 AgdaAny
v10
du_'8853''45'cong_3666 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8853''45'cong_3666 :: T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8853''45'cong_3666 T_BooleanAlgebra_698
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8
  = ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
      (\ AgdaAny
v9 AgdaAny
v10 AgdaAny
v11 ->
         (T__IsRelatedTo__26 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T__IsRelatedTo__26 -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 AgdaAny
v11)
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v3 AgdaAny
v5) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v4 AgdaAny
v6)
      (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
            ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                  ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
         ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v3 AgdaAny
v5)
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v3 AgdaAny
v5)
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v3 AgdaAny
v5)))
         ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v4 AgdaAny
v6)
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
               ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                  ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                     ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                        ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                           ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v3 AgdaAny
v5)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v3 AgdaAny
v5)))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v4 AgdaAny
v6)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v4 AgdaAny
v6)))
            ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v4 AgdaAny
v6)
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_372
               (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                  ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                     ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                        ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                           ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                              ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
               (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
                  ((T_IsLattice_3070 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
                     T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                     ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                        ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                           ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))))
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v4 AgdaAny
v6)
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v4 AgdaAny
v6)))
               ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v4 AgdaAny
v6) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v4 AgdaAny
v6)
               (((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_494
                  (((AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                     ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                        ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                           ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                              ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                 ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                    T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                    (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
                  ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v4 AgdaAny
v6))
               ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny
v4 AgdaAny
v6))
            ((T_BooleanAlgebra_698
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_helper_3660 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v3 AgdaAny
v5)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v4 AgdaAny
v6)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v3 AgdaAny
v5)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v4 AgdaAny
v6)
               ((AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Base.du__'10216'_'10217'__240 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v7)
                  ((T_IsLattice_3070
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> T_IsLattice_3070
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                     T_IsLattice_3070
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'cong_3098
                     (T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                        ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe
                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                           ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
                     AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 AgdaAny
v6)
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v8))
               ((AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Base.du__'10216'_'10217'__240 (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v7)
                  ((T_IsLattice_3070
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> T_IsLattice_3070
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                     T_IsLattice_3070
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'cong_3104
                     (T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                        ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe
                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                           ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
                     AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 AgdaAny
v6)
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v8))))
         ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny
v3 AgdaAny
v5))
-- Algebra.Lattice.Properties.BooleanAlgebra.XorRing.⊕-comm
d_'8853''45'comm_3680 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
d_'8853''45'comm_3680 :: ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8853''45'comm_3680 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6
  = T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8853''45'comm_3680 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6
du_'8853''45'comm_3680 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du_'8853''45'comm_3680 :: T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8853''45'comm_3680 T_BooleanAlgebra_698
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny
v3 AgdaAny
v4
  = ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
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-> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
      (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
         (T__IsRelatedTo__26 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T__IsRelatedTo__26 -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 AgdaAny
v7)
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v3 AgdaAny
v4) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v4 AgdaAny
v3)
      (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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coe
         (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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forall a b. a -> b
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            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
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-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
            ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                  ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
         ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v3 AgdaAny
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         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
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-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v3 AgdaAny
v4)
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v3 AgdaAny
v4)))
         ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v4 AgdaAny
v3)
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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 -> T__IsRelatedTo__26
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-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
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-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
               ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                  ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                     ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                        ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                           ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
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               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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v3 AgdaAny
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coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
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-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v3 AgdaAny
v4)))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v4 AgdaAny
v3)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v4 AgdaAny
v3)))
            ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v4 AgdaAny
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            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_372
               (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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                  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                  ((T_IsEquivalence_28
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-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                     ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                        ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                           ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                              ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
               (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
                  ((T_IsLattice_3070 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
                     T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                     ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                        ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                           ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))))
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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forall a b. a -> b
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                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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v4 AgdaAny
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                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
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coe
                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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v4 AgdaAny
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               ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
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               (((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny)
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forall a b. a -> b
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                  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_494
                  (((AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                     ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                        ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                           ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                              ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                 ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                    T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                    (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
                  ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
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               ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
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forall a b. a -> b
coe
               T_BooleanAlgebra_698
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du_helper_3660 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
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v0)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v3 AgdaAny
v4)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v4 AgdaAny
v3)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v3 AgdaAny
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               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v4 AgdaAny
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               ((T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny)
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forall a b. a -> b
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                  T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'comm_3094
                  (T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
                  AgdaAny
v3 AgdaAny
v4)
               ((T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'comm_3100
                  (T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
                  AgdaAny
v3 AgdaAny
v4)))
         ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny
v3 AgdaAny
v4))
-- Algebra.Lattice.Properties.BooleanAlgebra.XorRing.¬-distribˡ-⊕
d_'172''45'distrib'737''45''8853'_3690 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
d_'172''45'distrib'737''45''8853'_3690 :: ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'172''45'distrib'737''45''8853'_3690 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6
  = T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'172''45'distrib'737''45''8853'_3690 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6
du_'172''45'distrib'737''45''8853'_3690 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du_'172''45'distrib'737''45''8853'_3690 :: T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'172''45'distrib'737''45''8853'_3690 T_BooleanAlgebra_698
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny
v3 AgdaAny
v4
  = ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
      (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
         (T__IsRelatedTo__26 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T__IsRelatedTo__26 -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 AgdaAny
v7)
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
         ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v3 AgdaAny
v4))
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         AgdaAny -> AgdaAny -> AgdaAny
v1 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v3)
         AgdaAny
v4)
      (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
            ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                  ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
            ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v3 AgdaAny
v4))
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v3 AgdaAny
v4)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v3 AgdaAny
v4))))
         ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            AgdaAny -> AgdaAny -> AgdaAny
v1 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v3)
            AgdaAny
v4)
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
               ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                  ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                     ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                        ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                           ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v3 AgdaAny
v4)
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v3 AgdaAny
v4))))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v3
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                        ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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coe
                           T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v3 AgdaAny
v4)))
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v4
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                        ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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coe
                           T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v3 AgdaAny
v4)))))
            ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               AgdaAny -> AgdaAny -> AgdaAny
v1 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v3)
               AgdaAny
v4)
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
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-> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
               (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                  ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                     ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                        ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                           ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                              ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v3
                        ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                           ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
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                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                        ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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coe
                           T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v3 AgdaAny
v4))))
               ((T_IsDistributiveLattice_3146
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_3146
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                  T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'distrib'691''45''8744'_3210
                  (T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                     ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> T_IsBooleanAlgebra_3224
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                        (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v3 AgdaAny
v4))
                  AgdaAny
v3 AgdaAny
v4)))
         ((T_IsBooleanAlgebra_3224
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsBooleanAlgebra_3224
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
            T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'172''45'cong_3250
            (T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
               (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
            ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v3 AgdaAny
v4)
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v3 AgdaAny
v4)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v3 AgdaAny
v4)))
            ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny
v3 AgdaAny
v4)))
-- Algebra.Lattice.Properties.BooleanAlgebra.XorRing._.lem
d_lem_3704 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_lem_3704 :: ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_lem_3704 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 ~AgdaAny -> AgdaAny -> AgdaAny
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 ~AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
du_lem_3704 T_BooleanAlgebra_698
v2 AgdaAny
v7 AgdaAny
v8
du_lem_3704 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny
du_lem_3704 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
du_lem_3704 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2
  = ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
      (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 ->
         (T__IsRelatedTo__26 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T__IsRelatedTo__26 -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 AgdaAny
v5)
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)))
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2))
      (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
            ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                  ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)))
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2)))
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2))
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
               ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                  ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                     ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                        ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                           ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1)
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2)))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1))
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2)))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2))
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
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-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
               (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                  ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                     ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                        ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                           ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                              ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1))
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2)))
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                  (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2)))
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
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               (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
                  (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                     ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                        ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                           ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                              ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                 ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                    T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                    (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                     (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
                        ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2)))
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2))
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2))
                  (((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_494
                     (((AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                        ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                           ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                              ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                                 ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                    T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                    ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                       T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                       (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
                        ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2)))
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8744''45'identity'737'_3546 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
                        ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2))))
               ((T_IsLattice_3070
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'cong'691'_3136
                  ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2))
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1))
                  ((T_BooleanAlgebra_698 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
                  ((T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny)
-> T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'complement'691'_3312
                     (T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                        (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
                     AgdaAny
v1)))
            ((T_IsDistributiveLattice_3146
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_3146
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
               T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'distrib'737''45''8744'_3208
               (T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                  ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> T_IsBooleanAlgebra_3224
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                     (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
               AgdaAny
v1 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2)))
         ((T_IsLattice_3070
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'cong'737'_3124
            ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
               ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                  ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                     (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
du_deMorgan'8321'_3614 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))))
-- Algebra.Lattice.Properties.BooleanAlgebra.XorRing.¬-distribʳ-⊕
d_'172''45'distrib'691''45''8853'_3714 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
d_'172''45'distrib'691''45''8853'_3714 :: ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'172''45'distrib'691''45''8853'_3714 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6
  = T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'172''45'distrib'691''45''8853'_3714 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6
du_'172''45'distrib'691''45''8853'_3714 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du_'172''45'distrib'691''45''8853'_3714 :: T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'172''45'distrib'691''45''8853'_3714 T_BooleanAlgebra_698
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny
v3 AgdaAny
v4
  = ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
      (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
         (T__IsRelatedTo__26 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T__IsRelatedTo__26 -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 AgdaAny
v7)
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
         ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v3 AgdaAny
v4))
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v3
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v4))
      (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
            ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                  ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
            ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v3 AgdaAny
v4))
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
            ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v4 AgdaAny
v3))
         ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v3
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v4))
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
               ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                  ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                     ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                        ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                           ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
               ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v4 AgdaAny
v3))
            ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               AgdaAny -> AgdaAny -> AgdaAny
v1 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v4)
               AgdaAny
v3)
            ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v3
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v4))
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
               (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                  ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                     ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                        ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                           ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                              ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
               ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  AgdaAny -> AgdaAny -> AgdaAny
v1 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v4)
                  AgdaAny
v3)
               ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v3
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v4))
               ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v3
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v4))
               (((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_494
                  (((AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                     ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                        ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                           ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                              ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                 ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                    T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                    (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
                  ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v3
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v4)))
               ((T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8853''45'comm_3680 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2)
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v4)
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))
            ((T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'172''45'distrib'737''45''8853'_3690 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2)
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))
         ((T_IsBooleanAlgebra_3224
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsBooleanAlgebra_3224
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
            T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'172''45'cong_3250
            (T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
               (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
            ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v3 AgdaAny
v4) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v4 AgdaAny
v3)
            ((T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8853''45'comm_3680 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))
-- Algebra.Lattice.Properties.BooleanAlgebra.XorRing.⊕-annihilates-¬
d_'8853''45'annihilates'45''172'_3724 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
d_'8853''45'annihilates'45''172'_3724 :: ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8853''45'annihilates'45''172'_3724 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6
  = T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8853''45'annihilates'45''172'_3724 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6
du_'8853''45'annihilates'45''172'_3724 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
du_'8853''45'annihilates'45''172'_3724 :: T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8853''45'annihilates'45''172'_3724 T_BooleanAlgebra_698
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny
v3 AgdaAny
v4
  = ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v3)
                  AgdaAny
v4)
               ((T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'172''45'distrib'737''45''8853'_3690 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2)
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v4))))
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'172''45'involutive_3606 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v3 AgdaAny
v4)))
-- Algebra.Lattice.Properties.BooleanAlgebra.XorRing.⊕-identityˡ
d_'8853''45'identity'737'_3730 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
d_'8853''45'identity'737'_3730 :: ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
d_'8853''45'identity'737'_3730 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5
  = T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
du_'8853''45'identity'737'_3730 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5
du_'8853''45'identity'737'_3730 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
du_'8853''45'identity'737'_3730 :: T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
du_'8853''45'identity'737'_3730 T_BooleanAlgebra_698
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny
v3
  = ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
      (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
         (T__IsRelatedTo__26 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T__IsRelatedTo__26 -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 AgdaAny
v6)
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         AgdaAny -> AgdaAny -> AgdaAny
v1 (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)) AgdaAny
v3)
      AgdaAny
v3
      (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
            ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                  ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
         ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            AgdaAny -> AgdaAny -> AgdaAny
v1 (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)) AgdaAny
v3)
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
               (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)) AgdaAny
v3)
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                  (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)) AgdaAny
v3)))
         AgdaAny
v3
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
               ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                  ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                     ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                        ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                           ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                  (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)) AgdaAny
v3)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                     (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)) AgdaAny
v3)))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v3
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                  (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
            AgdaAny
v3
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
               (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                  ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                     ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                        ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                           ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                              ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v3
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                     (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v3
                  (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
               AgdaAny
v3
               (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
                  (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                     ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                        ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                           ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                              ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                 ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                    T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                    (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v3
                     (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
                  AgdaAny
v3 AgdaAny
v3
                  (((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_494
                     (((AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                        ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                           ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                              ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                                 ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                    T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                    ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                       T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                       (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
                     (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3))
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8743''45'identity'691'_3534 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)))
               ((T_IsLattice_3070
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'cong'737'_3124
                  ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                     (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
                  ((T_BooleanAlgebra_698 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
                  ((T_BooleanAlgebra_698 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny
du_'172''8869''8776''8868'_3602 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
            ((T_BooleanAlgebra_698
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_helper_3660 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                  (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)) AgdaAny
v3)
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                  (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)) AgdaAny
v3)
               ((T_BooleanAlgebra_698 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8744''45'identity'737'_3546 T_BooleanAlgebra_698
v0 AgdaAny
v3)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8743''45'zero'737'_3554 T_BooleanAlgebra_698
v0 AgdaAny
v3)))
         ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            AgdaAny -> AgdaAny -> AgdaAny
v2 (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
            AgdaAny
v3))
-- Algebra.Lattice.Properties.BooleanAlgebra.XorRing.⊕-identityʳ
d_'8853''45'identity'691'_3734 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
d_'8853''45'identity'691'_3734 :: ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
d_'8853''45'identity'691'_3734 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5
  = T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
du_'8853''45'identity'691'_3734 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5
du_'8853''45'identity'691'_3734 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
du_'8853''45'identity'691'_3734 :: T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
du_'8853''45'identity'691'_3734 T_BooleanAlgebra_698
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny
v3
  = (AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Base.du__'10216'_'10217'__240
      ((T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8853''45'comm_3680 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
         ((T_BooleanAlgebra_698 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
      ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
         (T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
            ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> T_IsLattice_3070
forall a b. a -> b
coe
               T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
               ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                  ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                     (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
         ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v3 (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
         ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            AgdaAny -> AgdaAny -> AgdaAny
v1 (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)) AgdaAny
v3)
         AgdaAny
v3)
      ((T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
du_'8853''45'identity'737'_3730 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2)
         (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3))
-- Algebra.Lattice.Properties.BooleanAlgebra.XorRing.⊕-identity
d_'8853''45'identity_3736 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8853''45'identity_3736 :: ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Σ_14
d_'8853''45'identity_3736 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4
  = T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Σ_14
du_'8853''45'identity_3736 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4
du_'8853''45'identity_3736 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8853''45'identity_3736 :: T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Σ_14
du_'8853''45'identity_3736 T_BooleanAlgebra_698
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny
v2
  = (AgdaAny -> AgdaAny -> T_Σ_14) -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      AgdaAny -> AgdaAny -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
      ((T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
du_'8853''45'identity'737'_3730 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2))
      ((T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
du_'8853''45'identity'691'_3734 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2))
-- Algebra.Lattice.Properties.BooleanAlgebra.XorRing.⊕-inverseˡ
d_'8853''45'inverse'737'_3738 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
d_'8853''45'inverse'737'_3738 :: ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
d_'8853''45'inverse'737'_3738 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5
  = T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
du_'8853''45'inverse'737'_3738 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5
du_'8853''45'inverse'737'_3738 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
du_'8853''45'inverse'737'_3738 :: T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
du_'8853''45'inverse'737'_3738 T_BooleanAlgebra_698
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny
v3
  = ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
      (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
         (T__IsRelatedTo__26 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T__IsRelatedTo__26 -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 AgdaAny
v6)
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v3 AgdaAny
v3)
      (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
            ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                  ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
         ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v3 AgdaAny
v3)
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v3 AgdaAny
v3)
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v3 AgdaAny
v3)))
         (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
               ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                  ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                     ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                        ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                           ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v3 AgdaAny
v3)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v3 AgdaAny
v3)))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v3
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v3))
            (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
               (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                  ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                     ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                        ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                           ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                              ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v3
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v3))
               (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
               (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
               (((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_494
                  (((AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                     ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                        ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                           ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                              ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                 ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                    T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                    (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
                  ((T_BooleanAlgebra_698 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
               ((T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny)
-> T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'complement'691'_3312
                  (T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                     (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
                  AgdaAny
v3))
            ((T_BooleanAlgebra_698
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_helper_3660 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v3 AgdaAny
v3)
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v3 AgdaAny
v3)
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
               ((T_Lattice_512 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Lattice_512 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8744''45'idem_318
                  ((T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_DistributiveLattice_598 -> T_Lattice_512
MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_678
                     ((T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.du_distributiveLattice_806
                        (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3))
               ((T_Lattice_512 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_Lattice_512 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8743''45'idem_294
                  ((T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_DistributiveLattice_598 -> T_Lattice_512
MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_678
                     ((T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.du_distributiveLattice_806
                        (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3))))
         ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny
v3 AgdaAny
v3))
-- Algebra.Lattice.Properties.BooleanAlgebra.XorRing.⊕-inverseʳ
d_'8853''45'inverse'691'_3742 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
d_'8853''45'inverse'691'_3742 :: ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
d_'8853''45'inverse'691'_3742 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5
  = T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
du_'8853''45'inverse'691'_3742 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5
du_'8853''45'inverse'691'_3742 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
du_'8853''45'inverse'691'_3742 :: T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
du_'8853''45'inverse'691'_3742 T_BooleanAlgebra_698
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny
v3
  = (AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Base.du__'10216'_'10217'__240
      ((T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8853''45'comm_3680 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
         (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3))
      ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
         (T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
            ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> T_IsLattice_3070
forall a b. a -> b
coe
               T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
               ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                  ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                     (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
         ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v3 AgdaAny
v3) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v3 AgdaAny
v3)
         (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
      ((T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
du_'8853''45'inverse'737'_3738 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3))
-- Algebra.Lattice.Properties.BooleanAlgebra.XorRing.⊕-inverse
d_'8853''45'inverse_3744 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8853''45'inverse_3744 :: ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Σ_14
d_'8853''45'inverse_3744 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4
  = T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Σ_14
du_'8853''45'inverse_3744 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4
du_'8853''45'inverse_3744 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8853''45'inverse_3744 :: T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Σ_14
du_'8853''45'inverse_3744 T_BooleanAlgebra_698
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny
v2
  = (AgdaAny -> AgdaAny -> T_Σ_14) -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      AgdaAny -> AgdaAny -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
      ((T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
du_'8853''45'inverse'737'_3738 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2))
      ((T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
du_'8853''45'inverse'691'_3742 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2))
-- Algebra.Lattice.Properties.BooleanAlgebra.XorRing.∧-distribˡ-⊕
d_'8743''45'distrib'737''45''8853'_3746 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'distrib'737''45''8853'_3746 :: ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'distrib'737''45''8853'_3746 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7
  = T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8743''45'distrib'737''45''8853'_3746 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7
du_'8743''45'distrib'737''45''8853'_3746 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'737''45''8853'_3746 :: T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8743''45'distrib'737''45''8853'_3746 T_BooleanAlgebra_698
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 AgdaAny
v5
  = ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
      (\ AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 ->
         (T__IsRelatedTo__26 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T__IsRelatedTo__26 -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 AgdaAny
v8)
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v3
         ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v4 AgdaAny
v5))
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         AgdaAny -> AgdaAny -> AgdaAny
v1
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v3 AgdaAny
v4)
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v3 AgdaAny
v5))
      (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
            ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                  ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v3
            ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v4 AgdaAny
v5))
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v3
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v4 AgdaAny
v5)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v4 AgdaAny
v5))))
         ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            AgdaAny -> AgdaAny -> AgdaAny
v1
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v3 AgdaAny
v4)
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v3 AgdaAny
v5))
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_372
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
               ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                  ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                     ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                        ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                           ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
               ((T_IsLattice_3070 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
                  T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                  ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v3
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v4 AgdaAny
v5)
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v4 AgdaAny
v5))))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v3
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v4 AgdaAny
v5))
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v4 AgdaAny
v5)))
            ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               AgdaAny -> AgdaAny -> AgdaAny
v1
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v3 AgdaAny
v4)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v3 AgdaAny
v5))
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
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forall a b. a -> b
coe
                     T_IsEquivalence_28
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                     ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                        ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
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forall a b. a -> b
coe
                           T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                           ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
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forall a b. a -> b
coe
                              T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
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forall a b. a -> b
coe
                                 T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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coe
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_372
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
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                        T_IsEquivalence_28
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                        ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                           ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
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forall a b. a -> b
coe
                              T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                              ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
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forall a b. a -> b
coe
                                 T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                 ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
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forall a b. a -> b
coe
                                    T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                    (T_BooleanAlgebra_698 -> AgdaAny
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coe T_BooleanAlgebra_698
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                  (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
                     ((T_IsLattice_3070 -> T_IsEquivalence_28)
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forall a b. a -> b
coe
                        T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                        ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
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forall a b. a -> b
coe
                           T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                           ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
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forall a b. a -> b
coe
                              T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                              ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
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forall a b. a -> b
coe
                                 T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                 (T_BooleanAlgebra_698 -> AgdaAny
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                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
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coe
                              T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
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                                 T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_372
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
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forall a b. a -> b
coe
                                 T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                                 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
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forall a b. a -> b
coe
                                    T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                                    ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
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forall a b. a -> b
coe
                                       T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                       ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
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forall a b. a -> b
coe
                                          T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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                        (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
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forall a b. a -> b
coe
                              T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
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coe
                                 T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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forall a b. a -> b
coe
                                    T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
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MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
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coe
                                    T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
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MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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                                          T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
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                                             T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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                                 T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                                 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
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                                    T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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                                       T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_372
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
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                                    T_IsEquivalence_28
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                                    ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                       T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                                       ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
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forall a b. a -> b
coe
                                          T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                                          ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
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forall a b. a -> b
coe
                                             T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                             ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
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forall a b. a -> b
coe
                                                T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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                              (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
                                 ((T_IsLattice_3070 -> T_IsEquivalence_28)
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forall a b. a -> b
coe
                                    T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                                    ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                       T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                                       ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
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forall a b. a -> b
coe
                                          T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                          ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
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forall a b. a -> b
coe
                                             T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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                                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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                                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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                                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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                                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
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                                       T_IsEquivalence_28
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                                       ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                          T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                                          ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
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forall a b. a -> b
coe
                                             T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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                                                T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
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forall a b. a -> b
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                                                   T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
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coe
                                             T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                                             ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
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coe
                                                T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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                                                   T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
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                                                      T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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                                       T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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                                          T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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                                             T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
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                                             T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726
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                                                T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726
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                                       T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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                                          T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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                                             T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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                                    ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_372
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
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coe
                                             T_IsEquivalence_28
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                                             ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                                T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                                                ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
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forall a b. a -> b
coe
                                                   T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                                                   ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
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forall a b. a -> b
coe
                                                      T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                                      ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
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forall a b. a -> b
coe
                                                         T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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                                       (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
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forall a b. a -> b
coe
                                             T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                                             ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
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forall a b. a -> b
coe
                                                T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                                                ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
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forall a b. a -> b
coe
                                                   T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                                   ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
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forall a b. a -> b
coe
                                                      T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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                                          T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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                                             T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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                                                T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726
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                                                T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726
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                                             T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726
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                                                   T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_494
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                                             ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
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                                                T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
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coe
                                                   T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
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                                                      T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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                                                         T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
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MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'cong'691'_3128
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MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
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MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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                                          T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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                                             T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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                                             T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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                                          T_IsDistributiveLattice_3146
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MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'distrib'737''45''8744'_3208
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MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
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forall a b. a -> b
coe
                                                T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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                                       T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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                                       T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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                                       T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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                                       T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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                                          T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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                                          T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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coe
                                       T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
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MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
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forall a b. a -> b
coe
                                             T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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coe
                                                T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                                ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
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forall a b. a -> b
coe
                                                   T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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                                          T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'cong'737'_3124
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coe
                                    T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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coe
                                       T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                       ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
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coe
                                          T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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                                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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                                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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                                 T_IsDistributiveLattice_3146 -> T_IsLattice_3070
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                                    T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
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                                       T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
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coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v4 AgdaAny
v5)))
            ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny
v4 AgdaAny
v5)))
-- Algebra.Lattice.Properties.BooleanAlgebra.XorRing._.lem₂
d_lem'8322'_3758 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_lem'8322'_3758 :: ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_lem'8322'_3758 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 ~AgdaAny -> AgdaAny -> AgdaAny
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7
  = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_lem'8322'_3758 T_BooleanAlgebra_698
v2 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7
du_lem'8322'_3758 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_lem'8322'_3758 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_lem'8322'_3758 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3
  = ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
      (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
         (T__IsRelatedTo__26 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T__IsRelatedTo__26 -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 AgdaAny
v6)
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v2 AgdaAny
v3))
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v2
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v3))
      (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_372
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
            ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                  ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
         (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
            ((T_IsLattice_3070 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
               T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
               ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                  ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                     ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                        (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))))
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v2 AgdaAny
v3))
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
            AgdaAny
v3)
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v2
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v3))
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
               ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                  ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                     ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                        ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                           ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
               AgdaAny
v3)
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v2 AgdaAny
v1)
               AgdaAny
v3)
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v2
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v3))
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
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-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
               (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
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 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                  ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                     ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                        ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                           ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                              ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v2 AgdaAny
v1)
                  AgdaAny
v3)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v2
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v3))
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v2
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v3))
               (((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_494
                  (((AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                     ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                        ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                           ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                              ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                 ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                    T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                    (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v2
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v3)))
               ((T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'assoc_3102
                  (T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
                  AgdaAny
v2 AgdaAny
v1 AgdaAny
v3))
            ((T_IsLattice_3070
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'cong'691'_3128
               ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                  ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                     ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                        (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v3)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v2 AgdaAny
v1)
               ((T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'comm_3100
                  (T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
                  AgdaAny
v1 AgdaAny
v2)))
         ((T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'assoc_3102
            (T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
               ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe
                  T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                  ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                     (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
            AgdaAny
v1 AgdaAny
v2 AgdaAny
v3))
-- Algebra.Lattice.Properties.BooleanAlgebra.XorRing._.lem₁
d_lem'8321'_3760 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_lem'8321'_3760 :: ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_lem'8321'_3760 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 ~AgdaAny -> AgdaAny -> AgdaAny
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7
  = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_lem'8321'_3760 T_BooleanAlgebra_698
v2 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7
du_lem'8321'_3760 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_lem'8321'_3760 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_lem'8321'_3760 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3
  = ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
      (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
         (T__IsRelatedTo__26 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T__IsRelatedTo__26 -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 AgdaAny
v6)
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v2 AgdaAny
v3))
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v3))
      (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_372
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
            ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                  ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
         (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
            ((T_IsLattice_3070 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
               T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
               ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                  ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                     ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                        (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))))
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v2 AgdaAny
v3))
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v1)
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v2 AgdaAny
v3))
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v3))
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
               ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                  ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                     ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                        ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                           ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v1)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v2 AgdaAny
v3))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v2 AgdaAny
v3)))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v3))
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
               (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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coe
                  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                  ((T_IsEquivalence_28
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-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                     ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                        ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                           ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                              ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
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forall a b. a -> b
coe
                                 T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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coe T_BooleanAlgebra_698
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               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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v1
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coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_372
                  (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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                     (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                     ((T_IsEquivalence_28
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-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                        ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                           ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                              ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                 ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
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forall a b. a -> b
coe
                                    T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                    (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
                  (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
                     ((T_IsLattice_3070 -> T_IsEquivalence_28)
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forall a b. a -> b
coe
                        T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                        ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                           ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
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forall a b. a -> b
coe
                              T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                              ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
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forall a b. a -> b
coe
                                 T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
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                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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                           T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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                  (((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny)
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                     (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_494
                     (((AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26)
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coe
                        (AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                        ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                           ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                              ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                                 ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
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forall a b. a -> b
coe
                                    T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                    ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
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forall a b. a -> b
coe
                                       T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                       (T_BooleanAlgebra_698 -> AgdaAny
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                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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                           T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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coe
                     T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'assoc_3102
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MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                        ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe
                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                           ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
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forall a b. a -> b
coe
                              T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'cong'737'_3124
                  ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
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                     T_IsDistributiveLattice_3146 -> T_IsLattice_3070
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                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
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                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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du_lem'8322'_3758 (T_BooleanAlgebra_698 -> AgdaAny
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MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'assoc_3102
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MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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-> AgdaAny -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe
                     T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                     ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
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                        T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'cong'691'_3128
            ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
               ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                  ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                     (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v2 AgdaAny
v3)
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v1)
            (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1)
            ((T_Lattice_512 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_Lattice_512 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Properties.Lattice.du_'8743''45'idem_294
               ((T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_DistributiveLattice_598 -> T_Lattice_512
MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_678
                  ((T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.du_distributiveLattice_806
                     (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
               (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1))))
-- Algebra.Lattice.Properties.BooleanAlgebra.XorRing._.lem₃
d_lem'8323'_3762 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_lem'8323'_3762 :: ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_lem'8323'_3762 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 ~AgdaAny -> AgdaAny -> AgdaAny
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7
  = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_lem'8323'_3762 T_BooleanAlgebra_698
v2 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7
du_lem'8323'_3762 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_lem'8323'_3762 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_lem'8323'_3762 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3
  = ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
      (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
         (T__IsRelatedTo__26 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T__IsRelatedTo__26 -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 AgdaAny
v6)
      (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v2 AgdaAny
v3))
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1))
      (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_372
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
            ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                  ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
         (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
            ((T_IsLattice_3070 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
               T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
               ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                  ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                     ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                        (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))))
         (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v2 AgdaAny
v3)
            (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v2 AgdaAny
v3))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1))
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
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-> AgdaAny
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_372
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
               ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                  ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                     ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                        ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                           ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
               ((T_IsLattice_3070 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
                  T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                  ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v2 AgdaAny
v3)
               (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v2 AgdaAny
v3)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1)))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v2 AgdaAny
v3))
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1))
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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-> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
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-> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_372
               (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
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 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                  ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                     ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                        ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                           ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                              ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
               (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
                  ((T_IsLattice_3070 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
                     T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                     ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                        ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                           ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))))
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v2 AgdaAny
v3)
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1)))
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v2 AgdaAny
v3)
                     AgdaAny
v1)
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
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               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v2 AgdaAny
v3))
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
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               (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
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-> AgdaAny
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-> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
                  (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                     ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                        ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                           ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                              ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                 ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                    T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                    (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                        ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v2 AgdaAny
v3)
                        AgdaAny
v1)
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1))
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
                        ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v2 AgdaAny
v3))
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
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                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
                        ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v2 AgdaAny
v3))
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1))
                  (((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_494
                     (((AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        (AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                        ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                           ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                              ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                                 ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                    T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                    ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                       T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                       (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
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                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                        ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
                           ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v2 AgdaAny
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                        ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
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forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
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                  ((T_IsLattice_3070
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'cong'691'_3128
                     ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                        ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                           ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
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                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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v1
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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                     ((T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'comm_3100
                        (T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                           ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe
                              T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                              ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
                        ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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v2 AgdaAny
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               ((T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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coe
                  T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'assoc_3102
                  (T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v2 AgdaAny
v3)
                  AgdaAny
v1 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1)))
            ((T_IsLattice_3070
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'cong'737'_3124
               ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                  ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                     ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                        (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v2 AgdaAny
v3)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1))
               ((T_BooleanAlgebra_698 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
               ((T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny)
-> T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'complement'691'_3312
                  (T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                     (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
                  AgdaAny
v1)))
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8743''45'zero'691'_3550 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v2 AgdaAny
v3)))
-- Algebra.Lattice.Properties.BooleanAlgebra.XorRing.∧-distribʳ-⊕
d_'8743''45'distrib'691''45''8853'_3764 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'distrib'691''45''8853'_3764 :: ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'distrib'691''45''8853'_3764 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4
  = T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8743''45'distrib'691''45''8853'_3764 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4
du_'8743''45'distrib'691''45''8853'_3764 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'691''45''8853'_3764 :: T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8743''45'distrib'691''45''8853'_3764 T_BooleanAlgebra_698
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny
v2
  = (T_Setoid_46
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny
     -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_Setoid_46
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny
    -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Consequences.Setoid.du_comm'8743'distr'737''8658'distr'691'_536
      ((T_Lattice_512 -> T_Setoid_46) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_Lattice_512 -> T_Setoid_46
MAlonzo.Code.Algebra.Lattice.Bundles.du_setoid_586
         ((T_DistributiveLattice_598 -> T_Lattice_512) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_DistributiveLattice_598 -> T_Lattice_512
MAlonzo.Code.Algebra.Lattice.Bundles.du_lattice_678
            ((T_BooleanAlgebra_698 -> T_DistributiveLattice_598)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> T_DistributiveLattice_598
MAlonzo.Code.Algebra.Lattice.Bundles.du_distributiveLattice_806
               (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) ((T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8853''45'cong_3666 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2))
      ((T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'comm_3100
         ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
            ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
               ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                  (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
      ((T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8743''45'distrib'737''45''8853'_3746 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1)
         ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2))
-- Algebra.Lattice.Properties.BooleanAlgebra.XorRing.∧-distrib-⊕
d_'8743''45'distrib'45''8853'_3766 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8743''45'distrib'45''8853'_3766 :: ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Σ_14
d_'8743''45'distrib'45''8853'_3766 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4
  = T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Σ_14
du_'8743''45'distrib'45''8853'_3766 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4
du_'8743''45'distrib'45''8853'_3766 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8743''45'distrib'45''8853'_3766 :: T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Σ_14
du_'8743''45'distrib'45''8853'_3766 T_BooleanAlgebra_698
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny
v2
  = (AgdaAny -> AgdaAny -> T_Σ_14) -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      AgdaAny -> AgdaAny -> T_Σ_14
MAlonzo.Code.Agda.Builtin.Sigma.C__'44'__32
      ((T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8743''45'distrib'737''45''8853'_3746 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1)
         ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2))
      ((T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8743''45'distrib'691''45''8853'_3764 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1)
         ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2))
-- Algebra.Lattice.Properties.BooleanAlgebra.XorRing.lemma₂
d_lemma'8322'_3776 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_lemma'8322'_3776 :: ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_lemma'8322'_3776 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 ~AgdaAny -> AgdaAny -> AgdaAny
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8
  = T_BooleanAlgebra_698
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_lemma'8322'_3776 T_BooleanAlgebra_698
v2 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 AgdaAny
v8
du_lemma'8322'_3776 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_lemma'8322'_3776 :: T_BooleanAlgebra_698
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_lemma'8322'_3776 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3 AgdaAny
v4
  = ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
      (\ AgdaAny
v5 AgdaAny
v6 AgdaAny
v7 ->
         (T__IsRelatedTo__26 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T__IsRelatedTo__26 -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 AgdaAny
v7)
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v3 AgdaAny
v4))
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v3)
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v2 AgdaAny
v3))
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v4)
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v2 AgdaAny
v4)))
      (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
            ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                  ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
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-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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v1 AgdaAny
v2)
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v3 AgdaAny
v4))
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
               AgdaAny
v3)
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
               AgdaAny
v4))
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v3)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v2 AgdaAny
v3))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v4)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v2 AgdaAny
v4)))
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
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-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
               ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                  ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                     ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                        ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                           ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
                  AgdaAny
v3)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
                  AgdaAny
v4))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v3)
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v2 AgdaAny
v3))
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v4)
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v2 AgdaAny
v4)))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
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                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
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               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v4)
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v2 AgdaAny
v4)))
            (((AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_494
               (((AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                  ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                     ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                        ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                           ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                              ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v4)
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v2 AgdaAny
v4))))
            ((AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Base.du__'10216'_'10217'__240
               ((T_IsDistributiveLattice_3146
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_3146
-> AgdaAny
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-> AgdaAny
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forall a b. a -> b
coe
                  T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'distrib'691''45''8743'_3206
                  (T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                     ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> T_IsBooleanAlgebra_3224
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                        (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
                  AgdaAny
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v1 AgdaAny
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               ((T_IsLattice_3070
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coe
                  T_IsLattice_3070
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MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'cong_3104
                  (T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
                     AgdaAny
v3)
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v3)
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v2 AgdaAny
v3))
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
                     AgdaAny
v4)
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v4)
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v2 AgdaAny
v4)))
               ((T_IsDistributiveLattice_3146
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_3146
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                  T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'distrib'691''45''8743'_3206
                  (T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                     ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> T_IsBooleanAlgebra_3224
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                        (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
                  AgdaAny
v4 AgdaAny
v1 AgdaAny
v2)))
         ((T_IsDistributiveLattice_3146
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsDistributiveLattice_3146
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3146
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'distrib'737''45''8743'_3204
            (T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
               ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> T_IsBooleanAlgebra_3224
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                  (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
            AgdaAny
v3 AgdaAny
v4))
-- Algebra.Lattice.Properties.BooleanAlgebra.XorRing.⊕-assoc
d_'8853''45'assoc_3786 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8853''45'assoc_3786 :: ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8853''45'assoc_3786 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7
  = T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8853''45'assoc_3786 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7
du_'8853''45'assoc_3786 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8853''45'assoc_3786 :: T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8853''45'assoc_3786 T_BooleanAlgebra_698
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny
v2 AgdaAny
v3 AgdaAny
v4 AgdaAny
v5
  = (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
      (T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
         ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> T_IsLattice_3070
forall a b. a -> b
coe
            T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
            ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
               ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                  (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v3 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v4 AgdaAny
v5)) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v3 AgdaAny
v4) AgdaAny
v5)
      (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
         (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
         (\ AgdaAny
v6 AgdaAny
v7 AgdaAny
v8 ->
            (T__IsRelatedTo__26 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T__IsRelatedTo__26 -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 AgdaAny
v8)
         ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v3 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v4 AgdaAny
v5)) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v3 AgdaAny
v4) AgdaAny
v5)
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
               ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                  ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                     ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                        ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                           ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
            ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v3 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v4 AgdaAny
v5))
            ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v3
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v4 AgdaAny
v5)
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v4 AgdaAny
v5))))
            ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v3 AgdaAny
v4) AgdaAny
v5)
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
               (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T__IsRelatedTo__26
-> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                  ((T_IsEquivalence_28
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                     ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                        ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                           ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                              ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
               ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny
v3
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v4 AgdaAny
v5)
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                        ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v4 AgdaAny
v5))))
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v3
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                        ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v4 AgdaAny
v5)
                        ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                           ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v4 AgdaAny
v5))))
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
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coe
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MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
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MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
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MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
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-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                                 ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                    T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                                    ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                       T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                                       ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                          T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                          ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                             T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                             (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
                           (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
                              ((T_IsLattice_3070 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
                                 T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                                 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                    T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                                    ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                       T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                       ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                          T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                          (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))))
                           ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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coe
                                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
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coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v3 AgdaAny
v4)
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v5)
                              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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coe
                                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                                    ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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coe
                                       T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                                       ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
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                                       ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
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                                          T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
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                                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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                                       T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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v0
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                                          T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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                                             T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
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                                       T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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                                          T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
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-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
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                                             T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
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                                          T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
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                           ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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                              T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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                              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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                                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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                                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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                                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
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                                       T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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                                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
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                                       T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
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                                          T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
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                                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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                                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
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                                       T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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                                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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                                       T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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                           ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
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v1 ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny -> AgdaAny
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                                 ((T_IsEquivalence_28
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forall a b. a -> b
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                                    T_IsEquivalence_28
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                                    ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                       T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                                       ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
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forall a b. a -> b
coe
                                          T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                                          ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
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                                             T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
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forall a b. a -> b
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                                                T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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                                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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                                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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                                       T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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                                          T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
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MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
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MAlonzo.Code.Relation.Binary.Structures.d_sym_38
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MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
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MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
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MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
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coe
                                                   T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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                                                      T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
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coe
                                                         T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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                                          T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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                                          T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
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MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
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                                                T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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                                                   T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
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forall a b. a -> b
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                                                      T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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                                       T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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                                             T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'cong_3104
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MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                                    ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
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forall a b. a -> b
coe
                                       T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                       ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
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coe
                                          T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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                                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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du_lem'8323'_3804 (T_BooleanAlgebra_698 -> AgdaAny
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du_lem'8324'_3808 (T_BooleanAlgebra_698 -> AgdaAny
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Relation.Binary.Structures.d_refl_36
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                        T_IsDistributiveLattice_3146 -> T_IsLattice_3070
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                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
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-- Algebra.Lattice.Properties.BooleanAlgebra.XorRing._.lem₁
d_lem'8321'_3798 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_lem'8321'_3798 :: ()
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d_lem'8321'_3798 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 ~AgdaAny -> AgdaAny -> AgdaAny
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7
  = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_lem'8321'_3798 T_BooleanAlgebra_698
v2 AgdaAny
v5 AgdaAny
v6 AgdaAny
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du_lem'8321'_3798 ::
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du_lem'8321'_3798 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_lem'8321'_3798 T_BooleanAlgebra_698
v0 AgdaAny
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 AgdaAny
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         (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_372
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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forall a b. a -> b
coe
            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
            ((T_IsEquivalence_28
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-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
               ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                  ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
         (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
            ((T_IsLattice_3070 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
               T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
               ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                  ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                     ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                        (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))))
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
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coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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v2)
               AgdaAny
v3)
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
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            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
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coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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v1 AgdaAny
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coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
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coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_372
            (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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coe
               (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
               ((T_IsEquivalence_28
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-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                  ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                     ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                        ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                           ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))))
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
               ((T_IsLattice_3070 -> T_IsEquivalence_28)
-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
                  T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                  ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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               (AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_494
               (((AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26)
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coe
                  (AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                  ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                     ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                        ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                           ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
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forall a b. a -> b
coe
                              T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                              ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
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forall a b. a -> b
coe
                                 T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                 (T_BooleanAlgebra_698 -> AgdaAny
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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               T_IsLattice_3070
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MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'cong'691'_3136
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MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
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MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'cong'737'_3124
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MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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du_deMorgan'8321'_3614 (T_BooleanAlgebra_698 -> AgdaAny
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MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'distrib'691''45''8743'_3206
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MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
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MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
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-- Algebra.Lattice.Properties.BooleanAlgebra.XorRing._.lem₂′
d_lem'8322''8242'_3800 ::
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d_lem'8322''8242'_3800 :: ()
-> ()
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d_lem'8322''8242'_3800 ~()
v0 ~()
v1 T_BooleanAlgebra_698
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v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ~AgdaAny
v7
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du_lem'8322''8242'_3800 T_BooleanAlgebra_698
v2 AgdaAny
v5 AgdaAny
v6
du_lem'8322''8242'_3800 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
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du_lem'8322''8242'_3800 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
du_lem'8322''8242'_3800 T_BooleanAlgebra_698
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 AgdaAny
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
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coe
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MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
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coe
                     T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
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                        T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
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MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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MAlonzo.Code.Relation.Binary.Structures.d_sym_38
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MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
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                     T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
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MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
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MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
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MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
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MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
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                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2) AgdaAny
v2)
                  (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
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               ((T_IsLattice_3070
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-> T_IsLattice_3070
-> AgdaAny
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-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
                  T_IsLattice_3070
-> AgdaAny
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MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'cong_3104
                  (T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1) AgdaAny
v1)
                  (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2) AgdaAny
v1)
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2))
                  ((T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny)
-> T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'complement'737'_3306
                     (T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                        (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
                     AgdaAny
v1)
                  ((T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'comm_3094
                     (T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                        ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe
                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                           ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                              (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2) AgdaAny
v1))
               ((T_IsLattice_3070
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLattice_3070
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'cong'737'_3124
                  ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1) AgdaAny
v2)
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2) AgdaAny
v2)
                  ((T_BooleanAlgebra_698 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
                  ((T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny)
-> T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'complement'737'_3306
                     (T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                        (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
                     AgdaAny
v2))))
         ((T_IsLattice_3070
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 -> AgdaAny
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 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> T_IsLattice_3070
-> AgdaAny
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-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_3070
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'cong_3104
            (T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
               ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe
                  T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                  ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                     (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
               (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
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                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
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            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1) AgdaAny
v2)
               (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1) AgdaAny
v2)
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8743''45'identity'737'_3538 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
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            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
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forall a b. a -> b
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               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8743''45'identity'691'_3534 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1)
                  AgdaAny
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-- Algebra.Lattice.Properties.BooleanAlgebra.XorRing._.lem₂
d_lem'8322'_3802 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_lem'8322'_3802 :: ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_lem'8322'_3802 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 ~AgdaAny -> AgdaAny -> AgdaAny
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7
  = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_lem'8322'_3802 T_BooleanAlgebra_698
v2 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7
du_lem'8322'_3802 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_lem'8322'_3802 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_lem'8322'_3802 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3
  = ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
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-> AgdaAny
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
      (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
         (T__IsRelatedTo__26 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
           T__IsRelatedTo__26 -> AgdaAny
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 AgdaAny
v6)
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
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         T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
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-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
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-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
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               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1
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-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
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-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
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         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
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            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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forall a b. a -> b
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
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v2)
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
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      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
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-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
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MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
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MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_372
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
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                     T_IsEquivalence_28
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
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forall a b. a -> b
coe
                        T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
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forall a b. a -> b
coe
                           T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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                              T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
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forall a b. a -> b
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                                 T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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               (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
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forall a b. a -> b
coe
                     T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
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forall a b. a -> b
coe
                        T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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coe
                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
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MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_494
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
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MAlonzo.Code.Relation.Binary.Structures.d_refl_36
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coe
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MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
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                              T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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                                 T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
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-- Algebra.Lattice.Properties.BooleanAlgebra.XorRing._.lem₃
d_lem'8323'_3804 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_lem'8323'_3804 :: ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
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-> AgdaAny
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d_lem'8323'_3804 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 ~AgdaAny -> AgdaAny -> AgdaAny
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7
  = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_lem'8323'_3804 T_BooleanAlgebra_698
v2 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7
du_lem'8323'_3804 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_lem'8323'_3804 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_lem'8323'_3804 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
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v5 AgdaAny
v6 ->
         (T__IsRelatedTo__26 -> AgdaAny) -> AgdaAny -> AgdaAny
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 AgdaAny
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
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forall a b. a -> b
coe
                  T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                  ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
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forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
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                     T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
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                        T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
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MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
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                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
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                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10216'_372
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
                  ((T_IsEquivalence_28
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-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_IsEquivalence_28
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_trans_40
                     ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                        ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                           ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
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forall a b. a -> b
coe
                              T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                              ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
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forall a b. a -> b
coe
                                 T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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forall a b. a -> b
coe T_BooleanAlgebra_698
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               (T_IsEquivalence_28 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_sym_38
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-> AgdaAny -> T_IsEquivalence_28
forall a b. a -> b
coe
                     T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                     ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                        ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                           ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
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forall a b. a -> b
coe
                              T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                              (T_BooleanAlgebra_698 -> AgdaAny
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                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
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coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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v1
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
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                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
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                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du__'8718'_494
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                     (AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                     ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
                        ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                           ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
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forall a b. a -> b
coe
                              T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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                                 T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                 ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
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                                    T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Function.Base.du__'10216'_'10217'__240
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                     T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'assoc_3096
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MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                        ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
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coe
                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                           ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
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coe
                              T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'cong_3104
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MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                        ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
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coe
                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                           ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
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coe
                              T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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v0
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                        ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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                           T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'assoc_3096
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MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
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forall a b. a -> b
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MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'distrib'737''45''8743'_3204
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MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
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MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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forall a b. a -> b
coe
            T_IsLattice_3070
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MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'cong'737'_3132
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               T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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coe
                  T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
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                     T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__298
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'cong'737'_3124
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                        T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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du_deMorgan'8321'_3614 (T_BooleanAlgebra_698 -> AgdaAny
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-- Algebra.Lattice.Properties.BooleanAlgebra.XorRing._.lem₄′
d_lem'8324''8242'_3806 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
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  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_lem'8324''8242'_3806 :: ()
-> ()
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d_lem'8324''8242'_3806 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 ~AgdaAny -> AgdaAny -> AgdaAny
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 ~AgdaAny
v5 AgdaAny
v6 AgdaAny
v7
  = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
du_lem'8324''8242'_3806 T_BooleanAlgebra_698
v2 AgdaAny
v6 AgdaAny
v7
du_lem'8324''8242'_3806 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny
du_lem'8324''8242'_3806 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
du_lem'8324''8242'_3806 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2
  = ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
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v5 ->
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 AgdaAny
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
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                        T_IsEquivalence_28
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
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forall a b. a -> b
coe
                           T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                           ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
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forall a b. a -> b
coe
                              T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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                                 T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
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                                    T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
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forall a b. a -> b
coe
                              T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                              ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
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coe
                                 T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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                                    T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                                    ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
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                                       T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
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                           (AgdaAny -> AgdaAny) -> AgdaAny -> T__IsRelatedTo__26
MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
                           ((T_IsEquivalence_28 -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
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                              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
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coe
                                 T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                                 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
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MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'complement'737'_3306
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MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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coe T_BooleanAlgebra_698
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                        (((AgdaAny -> AgdaAny -> AgdaAny)
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                           (AgdaAny -> AgdaAny -> AgdaAny)
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MAlonzo.Code.Function.Base.du_'8739'_'10217''45'__298
                           (\ AgdaAny
v3 AgdaAny
v4 -> AgdaAny
v4)
                           ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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forall a b. a -> b
coe
                              T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
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                           ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2) AgdaAny
v2)
                           (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
                     ((T_IsLattice_3070
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-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_IsLattice_3070
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MAlonzo.Code.Algebra.Lattice.Structures.du_'8743''45'cong'737'_3124
                        ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                           ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                              T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                              ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                                 T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                                 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
                        ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
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                           T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
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-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
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v2)
                        ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                           ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2) AgdaAny
v2)
                        ((T_BooleanAlgebra_698 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
                        ((T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny)
-> T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_IsBooleanAlgebra_3224 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'complement'737'_3306
                           (T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                              (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
                           AgdaAny
v2))))
               ((T_BooleanAlgebra_698
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-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_lemma'8322'_3776 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
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                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
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coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2)
                  (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2)))
            ((AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               AgdaAny -> (AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny -> AgdaAny
MAlonzo.Code.Function.Base.du__'10216'_'10217'__240
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
du_deMorgan'8322'_3634 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v1) (AgdaAny -> AgdaAny
forall a b. a -> b
coe AgdaAny
v2))
               ((T_IsLattice_3070
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-> T_IsLattice_3070
-> AgdaAny
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forall a b. a -> b
coe
                  T_IsLattice_3070
-> AgdaAny
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MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'cong_3098
                  (T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
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                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2))
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
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                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
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                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
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                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
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                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                        ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
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coe
                           T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
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                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
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               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
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                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'172''45'involutive_3606 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
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         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
du_deMorgan'8321'_3614 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
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-- Algebra.Lattice.Properties.BooleanAlgebra.XorRing._.lem₄
d_lem'8324'_3808 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_lem'8324'_3808 :: ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_lem'8324'_3808 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 ~AgdaAny -> AgdaAny -> AgdaAny
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7
  = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_lem'8324'_3808 T_BooleanAlgebra_698
v2 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7
du_lem'8324'_3808 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_lem'8324'_3808 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_lem'8324'_3808 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2 AgdaAny
v3
  = ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
      (\ AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 ->
         (T__IsRelatedTo__26 -> AgdaAny) -> AgdaAny -> AgdaAny
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 AgdaAny
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
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coe
            T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1
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-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
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               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
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coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v2 AgdaAny
v3)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
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                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
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                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v2 AgdaAny
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      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
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            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
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forall a b. a -> b
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MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
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      (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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         (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_step'45''8776''45''10217'_370
         (((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
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 -> T__IsRelatedTo__26
 -> T__IsRelatedTo__26)
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forall a b. a -> b
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            (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_'8764''45'go_40
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
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MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
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MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
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MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
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                     T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
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                        T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
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MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
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MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
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MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
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MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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MAlonzo.Code.Relation.Binary.Structures.d_sym_38
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MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
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MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
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MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_stop_54
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                              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
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MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
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                                    T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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                                       T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
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MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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MAlonzo.Code.Algebra.Lattice.Structures.d_'8744''45'assoc_3096
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MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'distrib'737''45''8743'_3204
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               T_IsLattice_3070
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MAlonzo.Code.Algebra.Lattice.Structures.du_'8744''45'cong'737'_3132
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MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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du_lem'8324''8242'_3806 (T_BooleanAlgebra_698 -> AgdaAny
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du_deMorgan'8321'_3614 (T_BooleanAlgebra_698 -> AgdaAny
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MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
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-- Algebra.Lattice.Properties.BooleanAlgebra.XorRing._.lem₅
d_lem'8325'_3810 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_lem'8325'_3810 :: ()
-> ()
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-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
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d_lem'8325'_3810 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 ~AgdaAny -> AgdaAny -> AgdaAny
v3 ~AgdaAny -> AgdaAny -> AgdaAny
v4 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7
  = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_lem'8325'_3810 T_BooleanAlgebra_698
v2 AgdaAny
v5 AgdaAny
v6 AgdaAny
v7
du_lem'8325'_3810 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_lem'8325'_3810 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_lem'8325'_3810 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
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  = ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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      (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
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MAlonzo.Code.Relation.Binary.Reasoning.Syntax.du_begin__46
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MAlonzo.Code.Relation.Binary.Reasoning.Base.Single.du_start_36 AgdaAny
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
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coe
                     T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
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forall a b. a -> b
coe
                        T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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                           T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
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coe
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MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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MAlonzo.Code.Relation.Binary.Structures.d_trans_40
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MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
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MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
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MAlonzo.Code.Relation.Binary.Structures.d_refl_36
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MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
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MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
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v0 AgdaAny
v3))
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1
                        ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2))
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v3))
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                        ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1)
                        ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2))
                     AgdaAny
v3))
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                        ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1)
                        ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2))
                     AgdaAny
v3)
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1
                        ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2))
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v3)))
               ((T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'comm_3100
                  (T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                     ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe
                        T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                        ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                           T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                           (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1
                        ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2))
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v3))
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                     ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                        T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                        ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1)
                        ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2))
                     AgdaAny
v3))))
         ((T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'assoc_3102
            (T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
               ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> T_IsDistributiveLattice_3146
forall a b. a -> b
coe
                  T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                  ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                     T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                     (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2))
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v3))
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1)
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v2))
               AgdaAny
v3)
            ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0
                  ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v1) AgdaAny
v2)
               ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0 AgdaAny
v3))))
-- Algebra.Lattice.Properties.BooleanAlgebra.XorRing.⊕-isMagma
d_'8853''45'isMagma_3812 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_'8853''45'isMagma_3812 :: ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_178
d_'8853''45'isMagma_3812 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4
  = T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_178
du_'8853''45'isMagma_3812 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4
du_'8853''45'isMagma_3812 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
du_'8853''45'isMagma_3812 :: T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_178
du_'8853''45'isMagma_3812 T_BooleanAlgebra_698
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny
v2
  = (T_IsEquivalence_28
 -> (AgdaAny
     -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsMagma_178)
-> AgdaAny -> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      T_IsEquivalence_28
-> (AgdaAny
    -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_178
MAlonzo.Code.Algebra.Structures.C_constructor_210
      ((T_IsLattice_3070 -> T_IsEquivalence_28) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
         ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
            ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
               ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                  (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
      ((T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8853''45'cong_3666 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2))
-- Algebra.Lattice.Properties.BooleanAlgebra.XorRing.⊕-isSemigroup
d_'8853''45'isSemigroup_3814 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_'8853''45'isSemigroup_3814 :: ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_488
d_'8853''45'isSemigroup_3814 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4
  = T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_488
du_'8853''45'isSemigroup_3814 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4
du_'8853''45'isSemigroup_3814 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
du_'8853''45'isSemigroup_3814 :: T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_488
du_'8853''45'isSemigroup_3814 T_BooleanAlgebra_698
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny
v2
  = (T_IsMagma_178
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_IsSemigroup_488)
-> AgdaAny -> AgdaAny -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_IsMagma_178
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> T_IsSemigroup_488
MAlonzo.Code.Algebra.Structures.C_constructor_522
      ((T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsMagma_178)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_178
du_'8853''45'isMagma_3812 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2))
      ((T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8853''45'assoc_3786 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2))
-- Algebra.Lattice.Properties.BooleanAlgebra.XorRing.⊕-⊥-isMonoid
d_'8853''45''8869''45'isMonoid_3816 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_'8853''45''8869''45'isMonoid_3816 :: ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMonoid_712
d_'8853''45''8869''45'isMonoid_3816 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4
  = T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMonoid_712
du_'8853''45''8869''45'isMonoid_3816 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4
du_'8853''45''8869''45'isMonoid_3816 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
du_'8853''45''8869''45'isMonoid_3816 :: T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMonoid_712
du_'8853''45''8869''45'isMonoid_3816 T_BooleanAlgebra_698
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny
v2
  = (T_IsSemigroup_488 -> T_Σ_14 -> T_IsMonoid_712)
-> AgdaAny -> AgdaAny -> T_IsMonoid_712
forall a b. a -> b
coe
      T_IsSemigroup_488 -> T_Σ_14 -> T_IsMonoid_712
MAlonzo.Code.Algebra.Structures.C_constructor_758
      ((T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsSemigroup_488)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_488
du_'8853''45'isSemigroup_3814 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2))
      ((T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Σ_14
du_'8853''45'identity_3736 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2))
-- Algebra.Lattice.Properties.BooleanAlgebra.XorRing.⊕-⊥-isGroup
d_'8853''45''8869''45'isGroup_3818 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074
d_'8853''45''8869''45'isGroup_3818 :: ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsGroup_1074
d_'8853''45''8869''45'isGroup_3818 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4
  = T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsGroup_1074
du_'8853''45''8869''45'isGroup_3818 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4
du_'8853''45''8869''45'isGroup_3818 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074
du_'8853''45''8869''45'isGroup_3818 :: T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsGroup_1074
du_'8853''45''8869''45'isGroup_3818 T_BooleanAlgebra_698
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny
v2
  = (T_IsMonoid_712
 -> T_Σ_14
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsGroup_1074)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsGroup_1074
forall a b. a -> b
coe
      T_IsMonoid_712
-> T_Σ_14
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsGroup_1074
MAlonzo.Code.Algebra.Structures.C_constructor_1164
      ((T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsMonoid_712)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMonoid_712
du_'8853''45''8869''45'isMonoid_3816 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2))
      ((T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Σ_14
du_'8853''45'inverse_3744 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2))
      ((AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe (\ AgdaAny
v3 AgdaAny
v4 AgdaAny
v5 -> AgdaAny
v5))
-- Algebra.Lattice.Properties.BooleanAlgebra.XorRing.⊕-⊥-isAbelianGroup
d_'8853''45''8869''45'isAbelianGroup_3820 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172
d_'8853''45''8869''45'isAbelianGroup_3820 :: ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1172
d_'8853''45''8869''45'isAbelianGroup_3820 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4
  = T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1172
du_'8853''45''8869''45'isAbelianGroup_3820 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4
du_'8853''45''8869''45'isAbelianGroup_3820 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172
du_'8853''45''8869''45'isAbelianGroup_3820 :: T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1172
du_'8853''45''8869''45'isAbelianGroup_3820 T_BooleanAlgebra_698
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny
v2
  = (T_IsGroup_1074
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsAbelianGroup_1172)
-> AgdaAny -> AgdaAny -> T_IsAbelianGroup_1172
forall a b. a -> b
coe
      T_IsGroup_1074
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsAbelianGroup_1172
MAlonzo.Code.Algebra.Structures.C_constructor_1252
      ((T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsGroup_1074)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsGroup_1074
du_'8853''45''8869''45'isGroup_3818 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2))
      ((T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8853''45'comm_3680 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2))
-- Algebra.Lattice.Properties.BooleanAlgebra.XorRing.⊕-∧-isRing
d_'8853''45''8743''45'isRing_3822 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740
d_'8853''45''8743''45'isRing_3822 :: ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsRing_2740
d_'8853''45''8743''45'isRing_3822 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4
  = T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsRing_2740
du_'8853''45''8743''45'isRing_3822 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4
du_'8853''45''8743''45'isRing_3822 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740
du_'8853''45''8743''45'isRing_3822 :: T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsRing_2740
du_'8853''45''8743''45'isRing_3822 T_BooleanAlgebra_698
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny
v2
  = (T_IsAbelianGroup_1172
 -> (AgdaAny
     -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
 -> T_Σ_14
 -> T_Σ_14
 -> T_IsRing_2740)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_IsRing_2740
forall a b. a -> b
coe
      T_IsAbelianGroup_1172
-> (AgdaAny
    -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_Σ_14
-> T_Σ_14
-> T_IsRing_2740
MAlonzo.Code.Algebra.Structures.C_constructor_2876
      ((T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsAbelianGroup_1172)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1172
du_'8853''45''8869''45'isAbelianGroup_3820 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1)
         ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2))
      ((T_IsLattice_3070
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_3070
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'cong_3104
         ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
            ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
               ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                  (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
      ((T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'assoc_3102
         ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
            ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
               ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                  (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
      ((T_BooleanAlgebra_698 -> T_Σ_14) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> T_Σ_14
du_'8743''45'identity_3540 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      ((T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Σ_14
du_'8743''45'distrib'45''8853'_3766 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2))
-- Algebra.Lattice.Properties.BooleanAlgebra.XorRing.⊕-∧-isCommutativeRing
d_'8853''45''8743''45'isCommutativeRing_3824 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888
d_'8853''45''8743''45'isCommutativeRing_3824 :: ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeRing_2888
d_'8853''45''8743''45'isCommutativeRing_3824 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4
  = T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeRing_2888
du_'8853''45''8743''45'isCommutativeRing_3824 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4
du_'8853''45''8743''45'isCommutativeRing_3824 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888
du_'8853''45''8743''45'isCommutativeRing_3824 :: T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeRing_2888
du_'8853''45''8743''45'isCommutativeRing_3824 T_BooleanAlgebra_698
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny
v2
  = (T_IsRing_2740
 -> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeRing_2888)
-> AgdaAny -> AgdaAny -> T_IsCommutativeRing_2888
forall a b. a -> b
coe
      T_IsRing_2740
-> (AgdaAny -> AgdaAny -> AgdaAny) -> T_IsCommutativeRing_2888
MAlonzo.Code.Algebra.Structures.C_constructor_3030
      ((T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsRing_2740)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsRing_2740
du_'8853''45''8743''45'isRing_3822 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2))
      ((T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_IsLattice_3070 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Structures.d_'8743''45'comm_3100
         ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
            T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
            ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
               T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
               ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                  T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                  (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
-- Algebra.Lattice.Properties.BooleanAlgebra.XorRing.⊕-∧-commutativeRing
d_'8853''45''8743''45'commutativeRing_3826 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Bundles.T_CommutativeRing_4126
d_'8853''45''8743''45'commutativeRing_3826 :: ()
-> ()
-> T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_CommutativeRing_4126
d_'8853''45''8743''45'commutativeRing_3826 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4
  = T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_CommutativeRing_4126
du_'8853''45''8743''45'commutativeRing_3826 T_BooleanAlgebra_698
v2 AgdaAny -> AgdaAny -> AgdaAny
v3 AgdaAny -> AgdaAny -> AgdaAny
v4
du_'8853''45''8743''45'commutativeRing_3826 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  (AgdaAny -> AgdaAny -> AgdaAny) ->
  MAlonzo.Code.Algebra.Bundles.T_CommutativeRing_4126
du_'8853''45''8743''45'commutativeRing_3826 :: T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_CommutativeRing_4126
du_'8853''45''8743''45'commutativeRing_3826 T_BooleanAlgebra_698
v0 AgdaAny -> AgdaAny -> AgdaAny
v1 AgdaAny -> AgdaAny -> AgdaAny
v2
  = ((AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> T_IsCommutativeRing_2888
 -> T_CommutativeRing_4126)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> T_CommutativeRing_4126
forall a b. a -> b
coe
      (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> T_IsCommutativeRing_2888
-> T_CommutativeRing_4126
MAlonzo.Code.Algebra.Bundles.C_constructor_4352 AgdaAny -> AgdaAny -> AgdaAny
v1
      (T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      (\ AgdaAny
v3 -> AgdaAny
v3)
      (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8869'_732 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      (T_BooleanAlgebra_698 -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'8868'_730 (T_BooleanAlgebra_698 -> T_BooleanAlgebra_698
forall a b. a -> b
coe T_BooleanAlgebra_698
v0))
      ((T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsCommutativeRing_2888)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeRing_2888
du_'8853''45''8743''45'isCommutativeRing_3824 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0) ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v1)
         ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe AgdaAny -> AgdaAny -> AgdaAny
v2))
-- Algebra.Lattice.Properties.BooleanAlgebra._⊕_
d__'8853'__3828 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny
d__'8853'__3828 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
d__'8853'__3828 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2
  = (T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
      ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
         T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
         ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2))
-- Algebra.Lattice.Properties.BooleanAlgebra.DefaultXorRing.¬-distribʳ-⊕
d_'172''45'distrib'691''45''8853'_3840 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_'172''45'distrib'691''45''8853'_3840 :: () -> () -> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
d_'172''45'distrib'691''45''8853'_3840 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
du_'172''45'distrib'691''45''8853'_3840 T_BooleanAlgebra_698
v2
du_'172''45'distrib'691''45''8853'_3840 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny
du_'172''45'distrib'691''45''8853'_3840 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
du_'172''45'distrib'691''45''8853'_3840 T_BooleanAlgebra_698
v0
  = (T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'172''45'distrib'691''45''8853'_3714 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2))))
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_28 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
              (T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> T_IsLattice_3070
forall a b. a -> b
coe
                    T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                    ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                       ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                          (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                    ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)))))
-- Algebra.Lattice.Properties.BooleanAlgebra.DefaultXorRing.¬-distribˡ-⊕
d_'172''45'distrib'737''45''8853'_3842 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_'172''45'distrib'737''45''8853'_3842 :: () -> () -> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
d_'172''45'distrib'737''45''8853'_3842 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
du_'172''45'distrib'737''45''8853'_3842 T_BooleanAlgebra_698
v2
du_'172''45'distrib'737''45''8853'_3842 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny
du_'172''45'distrib'737''45''8853'_3842 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
du_'172''45'distrib'737''45''8853'_3842 T_BooleanAlgebra_698
v0
  = (T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'172''45'distrib'737''45''8853'_3690 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2))))
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_28 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
              (T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> T_IsLattice_3070
forall a b. a -> b
coe
                    T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                    ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                       ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                          (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                    ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)))))
-- Algebra.Lattice.Properties.BooleanAlgebra.DefaultXorRing.∧-distrib-⊕
d_'8743''45'distrib'45''8853'_3844 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8743''45'distrib'45''8853'_3844 :: () -> () -> T_BooleanAlgebra_698 -> T_Σ_14
d_'8743''45'distrib'45''8853'_3844 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_Σ_14
du_'8743''45'distrib'45''8853'_3844 T_BooleanAlgebra_698
v2
du_'8743''45'distrib'45''8853'_3844 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8743''45'distrib'45''8853'_3844 :: T_BooleanAlgebra_698 -> T_Σ_14
du_'8743''45'distrib'45''8853'_3844 T_BooleanAlgebra_698
v0
  = (T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Σ_14
du_'8743''45'distrib'45''8853'_3766 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2))))
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_28 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
              (T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> T_IsLattice_3070
forall a b. a -> b
coe
                    T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                    ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                       ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                          (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                    ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)))))
-- Algebra.Lattice.Properties.BooleanAlgebra.DefaultXorRing.∧-distribʳ-⊕
d_'8743''45'distrib'691''45''8853'_3846 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'distrib'691''45''8853'_3846 :: ()
-> ()
-> T_BooleanAlgebra_698
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'distrib'691''45''8853'_3846 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'691''45''8853'_3846 T_BooleanAlgebra_698
v2
du_'8743''45'distrib'691''45''8853'_3846 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'691''45''8853'_3846 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'691''45''8853'_3846 T_BooleanAlgebra_698
v0
  = (T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8743''45'distrib'691''45''8853'_3764 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2))))
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_28 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
              (T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> T_IsLattice_3070
forall a b. a -> b
coe
                    T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                    ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                       ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                          (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                    ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)))))
-- Algebra.Lattice.Properties.BooleanAlgebra.DefaultXorRing.∧-distribˡ-⊕
d_'8743''45'distrib'737''45''8853'_3848 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8743''45'distrib'737''45''8853'_3848 :: ()
-> ()
-> T_BooleanAlgebra_698
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8743''45'distrib'737''45''8853'_3848 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'737''45''8853'_3848 T_BooleanAlgebra_698
v2
du_'8743''45'distrib'737''45''8853'_3848 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'737''45''8853'_3848 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8743''45'distrib'737''45''8853'_3848 T_BooleanAlgebra_698
v0
  = (T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8743''45'distrib'737''45''8853'_3746 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2))))
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_28 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
              (T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> T_IsLattice_3070
forall a b. a -> b
coe
                    T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                    ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                       ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                          (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                    ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)))))
-- Algebra.Lattice.Properties.BooleanAlgebra.DefaultXorRing.⊕-annihilates-¬
d_'8853''45'annihilates'45''172'_3850 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_'8853''45'annihilates'45''172'_3850 :: () -> () -> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8853''45'annihilates'45''172'_3850 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8853''45'annihilates'45''172'_3850 T_BooleanAlgebra_698
v2
du_'8853''45'annihilates'45''172'_3850 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny
du_'8853''45'annihilates'45''172'_3850 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8853''45'annihilates'45''172'_3850 T_BooleanAlgebra_698
v0
  = (T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8853''45'annihilates'45''172'_3724 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2))))
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_28 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
              (T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> T_IsLattice_3070
forall a b. a -> b
coe
                    T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                    ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                       ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                          (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                    ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)))))
-- Algebra.Lattice.Properties.BooleanAlgebra.DefaultXorRing.⊕-assoc
d_'8853''45'assoc_3852 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8853''45'assoc_3852 :: ()
-> ()
-> T_BooleanAlgebra_698
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8853''45'assoc_3852 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8853''45'assoc_3852 T_BooleanAlgebra_698
v2
du_'8853''45'assoc_3852 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8853''45'assoc_3852 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8853''45'assoc_3852 T_BooleanAlgebra_698
v0
  = (T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8853''45'assoc_3786 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2))))
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_28 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
              (T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> T_IsLattice_3070
forall a b. a -> b
coe
                    T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                    ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                       ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                          (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                    ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)))))
-- Algebra.Lattice.Properties.BooleanAlgebra.DefaultXorRing.⊕-comm
d_'8853''45'comm_3854 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny
d_'8853''45'comm_3854 :: () -> () -> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
d_'8853''45'comm_3854 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8853''45'comm_3854 T_BooleanAlgebra_698
v2
du_'8853''45'comm_3854 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny -> AgdaAny
du_'8853''45'comm_3854 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
du_'8853''45'comm_3854 T_BooleanAlgebra_698
v0
  = (T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8853''45'comm_3680 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2))))
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_28 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
              (T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> T_IsLattice_3070
forall a b. a -> b
coe
                    T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                    ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                       ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                          (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                    ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)))))
-- Algebra.Lattice.Properties.BooleanAlgebra.DefaultXorRing.⊕-cong
d_'8853''45'cong_3856 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
d_'8853''45'cong_3856 :: ()
-> ()
-> T_BooleanAlgebra_698
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
d_'8853''45'cong_3856 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 = T_BooleanAlgebra_698
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8853''45'cong_3856 T_BooleanAlgebra_698
v2
du_'8853''45'cong_3856 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny ->
  AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
du_'8853''45'cong_3856 :: T_BooleanAlgebra_698
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8853''45'cong_3856 T_BooleanAlgebra_698
v0
  = (T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
forall a b. a -> b
coe
      T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
-> AgdaAny
du_'8853''45'cong_3666 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2))))
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_28 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
              (T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> T_IsLattice_3070
forall a b. a -> b
coe
                    T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                    ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                       ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                          (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                    ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)))))
-- Algebra.Lattice.Properties.BooleanAlgebra.DefaultXorRing.⊕-identity
d_'8853''45'identity_3858 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8853''45'identity_3858 :: () -> () -> T_BooleanAlgebra_698 -> T_Σ_14
d_'8853''45'identity_3858 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_Σ_14
du_'8853''45'identity_3858 T_BooleanAlgebra_698
v2
du_'8853''45'identity_3858 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8853''45'identity_3858 :: T_BooleanAlgebra_698 -> T_Σ_14
du_'8853''45'identity_3858 T_BooleanAlgebra_698
v0
  = (T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Σ_14
du_'8853''45'identity_3736 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2))))
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_28 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
              (T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> T_IsLattice_3070
forall a b. a -> b
coe
                    T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                    ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                       ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                          (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                    ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)))))
-- Algebra.Lattice.Properties.BooleanAlgebra.DefaultXorRing.⊕-identityʳ
d_'8853''45'identity'691'_3860 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny
d_'8853''45'identity'691'_3860 :: () -> () -> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
d_'8853''45'identity'691'_3860 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8853''45'identity'691'_3860 T_BooleanAlgebra_698
v2
du_'8853''45'identity'691'_3860 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny
du_'8853''45'identity'691'_3860 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8853''45'identity'691'_3860 T_BooleanAlgebra_698
v0
  = (T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
du_'8853''45'identity'691'_3734 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2))))
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_28 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
              (T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> T_IsLattice_3070
forall a b. a -> b
coe
                    T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                    ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                       ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                          (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                    ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)))))
-- Algebra.Lattice.Properties.BooleanAlgebra.DefaultXorRing.⊕-identityˡ
d_'8853''45'identity'737'_3862 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny
d_'8853''45'identity'737'_3862 :: () -> () -> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
d_'8853''45'identity'737'_3862 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8853''45'identity'737'_3862 T_BooleanAlgebra_698
v2
du_'8853''45'identity'737'_3862 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny
du_'8853''45'identity'737'_3862 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8853''45'identity'737'_3862 T_BooleanAlgebra_698
v0
  = (T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
du_'8853''45'identity'737'_3730 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2))))
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_28 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
              (T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> T_IsLattice_3070
forall a b. a -> b
coe
                    T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                    ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                       ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                          (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                    ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)))))
-- Algebra.Lattice.Properties.BooleanAlgebra.DefaultXorRing.⊕-inverse
d_'8853''45'inverse_3864 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
d_'8853''45'inverse_3864 :: () -> () -> T_BooleanAlgebra_698 -> T_Σ_14
d_'8853''45'inverse_3864 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 = T_BooleanAlgebra_698 -> T_Σ_14
du_'8853''45'inverse_3864 T_BooleanAlgebra_698
v2
du_'8853''45'inverse_3864 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Agda.Builtin.Sigma.T_Σ_14
du_'8853''45'inverse_3864 :: T_BooleanAlgebra_698 -> T_Σ_14
du_'8853''45'inverse_3864 T_BooleanAlgebra_698
v0
  = (T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> T_Σ_14)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_Σ_14
forall a b. a -> b
coe
      T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_Σ_14
du_'8853''45'inverse_3744 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2))))
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_28 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
              (T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> T_IsLattice_3070
forall a b. a -> b
coe
                    T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                    ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                       ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                          (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                    ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)))))
-- Algebra.Lattice.Properties.BooleanAlgebra.DefaultXorRing.⊕-inverseʳ
d_'8853''45'inverse'691'_3866 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny
d_'8853''45'inverse'691'_3866 :: () -> () -> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
d_'8853''45'inverse'691'_3866 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8853''45'inverse'691'_3866 T_BooleanAlgebra_698
v2
du_'8853''45'inverse'691'_3866 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny
du_'8853''45'inverse'691'_3866 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8853''45'inverse'691'_3866 T_BooleanAlgebra_698
v0
  = (T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
du_'8853''45'inverse'691'_3742 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2))))
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_28 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
              (T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> T_IsLattice_3070
forall a b. a -> b
coe
                    T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                    ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                       ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                          (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                    ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)))))
-- Algebra.Lattice.Properties.BooleanAlgebra.DefaultXorRing.⊕-inverseˡ
d_'8853''45'inverse'737'_3868 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny
d_'8853''45'inverse'737'_3868 :: () -> () -> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
d_'8853''45'inverse'737'_3868 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8853''45'inverse'737'_3868 T_BooleanAlgebra_698
v2
du_'8853''45'inverse'737'_3868 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny -> AgdaAny
du_'8853''45'inverse'737'_3868 :: T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
du_'8853''45'inverse'737'_3868 T_BooleanAlgebra_698
v0
  = (T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> AgdaAny
 -> AgdaAny)
-> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
      T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> AgdaAny
-> AgdaAny
du_'8853''45'inverse'737'_3738 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2))))
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_28 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
              (T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> T_IsLattice_3070
forall a b. a -> b
coe
                    T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                    ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                       ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                          (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                    ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)))))
-- Algebra.Lattice.Properties.BooleanAlgebra.DefaultXorRing.⊕-isMagma
d_'8853''45'isMagma_3870 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
d_'8853''45'isMagma_3870 :: () -> () -> T_BooleanAlgebra_698 -> T_IsMagma_178
d_'8853''45'isMagma_3870 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2 = T_BooleanAlgebra_698 -> T_IsMagma_178
du_'8853''45'isMagma_3870 T_BooleanAlgebra_698
v2
du_'8853''45'isMagma_3870 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsMagma_178
du_'8853''45'isMagma_3870 :: T_BooleanAlgebra_698 -> T_IsMagma_178
du_'8853''45'isMagma_3870 T_BooleanAlgebra_698
v0
  = (T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsMagma_178)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsMagma_178
forall a b. a -> b
coe
      T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMagma_178
du_'8853''45'isMagma_3812 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2))))
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_28 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
              (T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> T_IsLattice_3070
forall a b. a -> b
coe
                    T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                    ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                       ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                          (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                    ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)))))
-- Algebra.Lattice.Properties.BooleanAlgebra.DefaultXorRing.⊕-isSemigroup
d_'8853''45'isSemigroup_3872 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
d_'8853''45'isSemigroup_3872 :: () -> () -> T_BooleanAlgebra_698 -> T_IsSemigroup_488
d_'8853''45'isSemigroup_3872 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_IsSemigroup_488
du_'8853''45'isSemigroup_3872 T_BooleanAlgebra_698
v2
du_'8853''45'isSemigroup_3872 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsSemigroup_488
du_'8853''45'isSemigroup_3872 :: T_BooleanAlgebra_698 -> T_IsSemigroup_488
du_'8853''45'isSemigroup_3872 T_BooleanAlgebra_698
v0
  = (T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsSemigroup_488)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsSemigroup_488
forall a b. a -> b
coe
      T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsSemigroup_488
du_'8853''45'isSemigroup_3814 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2))))
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_28 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
              (T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> T_IsLattice_3070
forall a b. a -> b
coe
                    T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                    ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                       ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                          (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                    ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)))))
-- Algebra.Lattice.Properties.BooleanAlgebra.DefaultXorRing.⊕-∧-commutativeRing
d_'8853''45''8743''45'commutativeRing_3874 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Bundles.T_CommutativeRing_4126
d_'8853''45''8743''45'commutativeRing_3874 :: () -> () -> T_BooleanAlgebra_698 -> T_CommutativeRing_4126
d_'8853''45''8743''45'commutativeRing_3874 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_CommutativeRing_4126
du_'8853''45''8743''45'commutativeRing_3874 T_BooleanAlgebra_698
v2
du_'8853''45''8743''45'commutativeRing_3874 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Bundles.T_CommutativeRing_4126
du_'8853''45''8743''45'commutativeRing_3874 :: T_BooleanAlgebra_698 -> T_CommutativeRing_4126
du_'8853''45''8743''45'commutativeRing_3874 T_BooleanAlgebra_698
v0
  = (T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> T_CommutativeRing_4126)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_CommutativeRing_4126
forall a b. a -> b
coe
      T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_CommutativeRing_4126
du_'8853''45''8743''45'commutativeRing_3826 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2))))
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_28 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
              (T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> T_IsLattice_3070
forall a b. a -> b
coe
                    T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                    ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                       ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                          (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                    ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)))))
-- Algebra.Lattice.Properties.BooleanAlgebra.DefaultXorRing.⊕-∧-isCommutativeRing
d_'8853''45''8743''45'isCommutativeRing_3876 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888
d_'8853''45''8743''45'isCommutativeRing_3876 :: () -> () -> T_BooleanAlgebra_698 -> T_IsCommutativeRing_2888
d_'8853''45''8743''45'isCommutativeRing_3876 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_IsCommutativeRing_2888
du_'8853''45''8743''45'isCommutativeRing_3876 T_BooleanAlgebra_698
v2
du_'8853''45''8743''45'isCommutativeRing_3876 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsCommutativeRing_2888
du_'8853''45''8743''45'isCommutativeRing_3876 :: T_BooleanAlgebra_698 -> T_IsCommutativeRing_2888
du_'8853''45''8743''45'isCommutativeRing_3876 T_BooleanAlgebra_698
v0
  = (T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsCommutativeRing_2888)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsCommutativeRing_2888
forall a b. a -> b
coe
      T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsCommutativeRing_2888
du_'8853''45''8743''45'isCommutativeRing_3824 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2))))
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_28 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
              (T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> T_IsLattice_3070
forall a b. a -> b
coe
                    T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                    ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                       ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                          (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                    ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)))))
-- Algebra.Lattice.Properties.BooleanAlgebra.DefaultXorRing.⊕-∧-isRing
d_'8853''45''8743''45'isRing_3878 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740
d_'8853''45''8743''45'isRing_3878 :: () -> () -> T_BooleanAlgebra_698 -> T_IsRing_2740
d_'8853''45''8743''45'isRing_3878 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_IsRing_2740
du_'8853''45''8743''45'isRing_3878 T_BooleanAlgebra_698
v2
du_'8853''45''8743''45'isRing_3878 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsRing_2740
du_'8853''45''8743''45'isRing_3878 :: T_BooleanAlgebra_698 -> T_IsRing_2740
du_'8853''45''8743''45'isRing_3878 T_BooleanAlgebra_698
v0
  = (T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsRing_2740)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsRing_2740
forall a b. a -> b
coe
      T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsRing_2740
du_'8853''45''8743''45'isRing_3822 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2))))
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_28 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
              (T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> T_IsLattice_3070
forall a b. a -> b
coe
                    T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                    ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                       ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                          (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                    ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)))))
-- Algebra.Lattice.Properties.BooleanAlgebra.DefaultXorRing.⊕-⊥-isAbelianGroup
d_'8853''45''8869''45'isAbelianGroup_3880 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172
d_'8853''45''8869''45'isAbelianGroup_3880 :: () -> () -> T_BooleanAlgebra_698 -> T_IsAbelianGroup_1172
d_'8853''45''8869''45'isAbelianGroup_3880 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_IsAbelianGroup_1172
du_'8853''45''8869''45'isAbelianGroup_3880 T_BooleanAlgebra_698
v2
du_'8853''45''8869''45'isAbelianGroup_3880 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsAbelianGroup_1172
du_'8853''45''8869''45'isAbelianGroup_3880 :: T_BooleanAlgebra_698 -> T_IsAbelianGroup_1172
du_'8853''45''8869''45'isAbelianGroup_3880 T_BooleanAlgebra_698
v0
  = (T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsAbelianGroup_1172)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsAbelianGroup_1172
forall a b. a -> b
coe
      T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsAbelianGroup_1172
du_'8853''45''8869''45'isAbelianGroup_3820 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2))))
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_28 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
              (T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> T_IsLattice_3070
forall a b. a -> b
coe
                    T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                    ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                       ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                          (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                    ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)))))
-- Algebra.Lattice.Properties.BooleanAlgebra.DefaultXorRing.⊕-⊥-isGroup
d_'8853''45''8869''45'isGroup_3882 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074
d_'8853''45''8869''45'isGroup_3882 :: () -> () -> T_BooleanAlgebra_698 -> T_IsGroup_1074
d_'8853''45''8869''45'isGroup_3882 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_IsGroup_1074
du_'8853''45''8869''45'isGroup_3882 T_BooleanAlgebra_698
v2
du_'8853''45''8869''45'isGroup_3882 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsGroup_1074
du_'8853''45''8869''45'isGroup_3882 :: T_BooleanAlgebra_698 -> T_IsGroup_1074
du_'8853''45''8869''45'isGroup_3882 T_BooleanAlgebra_698
v0
  = (T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsGroup_1074)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsGroup_1074
forall a b. a -> b
coe
      T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsGroup_1074
du_'8853''45''8869''45'isGroup_3818 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2))))
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_28 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
              (T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> T_IsLattice_3070
forall a b. a -> b
coe
                    T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                    ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                       ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                          (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                    ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)))))
-- Algebra.Lattice.Properties.BooleanAlgebra.DefaultXorRing.⊕-⊥-isMonoid
d_'8853''45''8869''45'isMonoid_3884 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
d_'8853''45''8869''45'isMonoid_3884 :: () -> () -> T_BooleanAlgebra_698 -> T_IsMonoid_712
d_'8853''45''8869''45'isMonoid_3884 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> T_IsMonoid_712
du_'8853''45''8869''45'isMonoid_3884 T_BooleanAlgebra_698
v2
du_'8853''45''8869''45'isMonoid_3884 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  MAlonzo.Code.Algebra.Structures.T_IsMonoid_712
du_'8853''45''8869''45'isMonoid_3884 :: T_BooleanAlgebra_698 -> T_IsMonoid_712
du_'8853''45''8869''45'isMonoid_3884 T_BooleanAlgebra_698
v0
  = (T_BooleanAlgebra_698
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> (AgdaAny -> AgdaAny -> AgdaAny)
 -> T_IsMonoid_712)
-> AgdaAny -> AgdaAny -> AgdaAny -> T_IsMonoid_712
forall a b. a -> b
coe
      T_BooleanAlgebra_698
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> (AgdaAny -> AgdaAny -> AgdaAny)
-> T_IsMonoid_712
du_'8853''45''8869''45'isMonoid_3816 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2))))
      ((AgdaAny -> AgdaAny -> AgdaAny) -> AgdaAny
forall a b. a -> b
coe
         (\ AgdaAny
v1 AgdaAny
v2 ->
            (T_IsEquivalence_28 -> AgdaAny -> AgdaAny)
-> T_IsEquivalence_28 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
              T_IsEquivalence_28 -> AgdaAny -> AgdaAny
MAlonzo.Code.Relation.Binary.Structures.d_refl_36
              (T_IsLattice_3070 -> T_IsEquivalence_28
MAlonzo.Code.Algebra.Lattice.Structures.d_isEquivalence_3092
                 ((T_IsDistributiveLattice_3146 -> T_IsLattice_3070)
-> AgdaAny -> T_IsLattice_3070
forall a b. a -> b
coe
                    T_IsDistributiveLattice_3146 -> T_IsLattice_3070
MAlonzo.Code.Algebra.Lattice.Structures.d_isLattice_3158
                    ((T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_IsBooleanAlgebra_3224 -> T_IsDistributiveLattice_3146
MAlonzo.Code.Algebra.Lattice.Structures.d_isDistributiveLattice_3244
                       ((T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224)
-> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                          T_BooleanAlgebra_698 -> T_IsBooleanAlgebra_3224
MAlonzo.Code.Algebra.Lattice.Bundles.d_isBooleanAlgebra_734
                          (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)))))
              ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                 T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8744'__724 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)
                 ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                    T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d_'172'__728 T_BooleanAlgebra_698
v0
                    ((T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny)
-> T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
forall a b. a -> b
coe
                       T_BooleanAlgebra_698 -> AgdaAny -> AgdaAny -> AgdaAny
MAlonzo.Code.Algebra.Lattice.Bundles.d__'8743'__726 T_BooleanAlgebra_698
v0 AgdaAny
v1 AgdaAny
v2)))))
-- Algebra.Lattice.Properties.BooleanAlgebra.⊥≉⊤
d_'8869''8777''8868'_3886 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny
d_'8869''8777''8868'_3886 :: () -> () -> T_BooleanAlgebra_698 -> AgdaAny
d_'8869''8777''8868'_3886 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> AgdaAny
du_'8869''8777''8868'_3886 T_BooleanAlgebra_698
v2
du_'8869''8777''8868'_3886 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny
du_'8869''8777''8868'_3886 :: T_BooleanAlgebra_698 -> AgdaAny
du_'8869''8777''8868'_3886 T_BooleanAlgebra_698
v0
  = (T_BooleanAlgebra_698 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny
du_'172''8869''8776''8868'_3602 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)
-- Algebra.Lattice.Properties.BooleanAlgebra.⊤≉⊥
d_'8868''8777''8869'_3888 ::
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Agda.Primitive.T_Level_18 ->
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny
d_'8868''8777''8869'_3888 :: () -> () -> T_BooleanAlgebra_698 -> AgdaAny
d_'8868''8777''8869'_3888 ~()
v0 ~()
v1 T_BooleanAlgebra_698
v2
  = T_BooleanAlgebra_698 -> AgdaAny
du_'8868''8777''8869'_3888 T_BooleanAlgebra_698
v2
du_'8868''8777''8869'_3888 ::
  MAlonzo.Code.Algebra.Lattice.Bundles.T_BooleanAlgebra_698 ->
  AgdaAny
du_'8868''8777''8869'_3888 :: T_BooleanAlgebra_698 -> AgdaAny
du_'8868''8777''8869'_3888 T_BooleanAlgebra_698
v0
  = (T_BooleanAlgebra_698 -> AgdaAny) -> AgdaAny -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698 -> AgdaAny
du_'172''8868''8776''8869'_3604 (T_BooleanAlgebra_698 -> AgdaAny
forall a b. a -> b
coe T_BooleanAlgebra_698
v0)