Safe Haskell	Safe-Inferred
Language	Haskell2010

MAlonzo.Code.Algebra.Structures

Documentation

d__DistributesOver__16 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → () Source #

d__DistributesOver'691'__18 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → () Source #

d__DistributesOver'737'__20 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → () Source #

d_AlmostLeftCancellative_30 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → AgdaAny → (AgdaAny → AgdaAny → AgdaAny) → () Source #

d_AlmostRightCancellative_32 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → AgdaAny → (AgdaAny → AgdaAny → AgdaAny) → () Source #

d_Alternative_34 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → () Source #

d_Associative_36 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → () Source #

d_Commutative_40 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → () Source #

d_Congruent'8321'_42 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny) → () Source #

d_Congruent'8322'_44 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → () Source #

d_Flexible_48 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → () Source #

d_Idempotent_50 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → () Source #

d_Identical_54 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → () Source #

d_Identity_56 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → AgdaAny → (AgdaAny → AgdaAny → AgdaAny) → () Source #

d_Inverse_60 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → AgdaAny → (AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → () Source #

d_LeftAlternative_66 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → () Source #

d_LeftBol_68 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → () Source #

d_LeftCongruent_72 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → () Source #

d_LeftDivides_76 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → () Source #

d_LeftDivides'691'_78 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → () Source #

d_LeftDivides'737'_80 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → () Source #

d_LeftIdentity_82 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → AgdaAny → (AgdaAny → AgdaAny → AgdaAny) → () Source #

d_LeftInverse_84 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → AgdaAny → (AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → () Source #

d_LeftSemimedial_88 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → () Source #

d_LeftZero_90 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → AgdaAny → (AgdaAny → AgdaAny → AgdaAny) → () Source #

d_Medial_92 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → () Source #

d_MiddleBol_94 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → () Source #

d_RightAlternative_96 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → () Source #

d_RightBol_98 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → () Source #

d_RightCongruent_102 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → () Source #

d_RightDivides_106 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → () Source #

d_RightDivides'691'_108 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → () Source #

d_RightDivides'737'_110 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → () Source #

d_RightIdentity_112 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → AgdaAny → (AgdaAny → AgdaAny → AgdaAny) → () Source #

d_RightInverse_114 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → AgdaAny → (AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → () Source #

d_RightSemimedial_118 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → () Source #

d_RightZero_120 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → AgdaAny → (AgdaAny → AgdaAny → AgdaAny) → () Source #

d_Selective_122 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → () Source #

d_Semimedial_126 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → () Source #

d_StarDestructive_128 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → () Source #

d_StarExpansive_130 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → AgdaAny → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → () Source #

d_StarLeftDestructive_132 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → () Source #

d_StarLeftExpansive_134 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → AgdaAny → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → () Source #

d_StarRightDestructive_136 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → () Source #

d_StarRightExpansive_138 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → AgdaAny → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → () Source #

d_Zero_140 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → AgdaAny → (AgdaAny → AgdaAny → AgdaAny) → () Source #

d_IsSuccessorSet_146 ∷ p → p → p → p → p → p → () Source #

data T_IsSuccessorSet_146 Source #

Constructors

C_constructor_174 T_IsEquivalence_28 (AgdaAny → AgdaAny → AgdaAny → AgdaAny)

d_isEquivalence_156 ∷ T_IsSuccessorSet_146 → T_IsEquivalence_28 Source #

d_suc'35''45'cong_158 ∷ T_IsSuccessorSet_146 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_isPartialEquivalence_162 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny) → AgdaAny → T_IsSuccessorSet_146 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_162 ∷ T_IsSuccessorSet_146 → T_IsPartialEquivalence_16 Source #

d_refl_164 ∷ T_IsSuccessorSet_146 → AgdaAny → AgdaAny Source #

d_reflexive_166 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny) → AgdaAny → T_IsSuccessorSet_146 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_166 ∷ T_IsSuccessorSet_146 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_sym_168 ∷ T_IsSuccessorSet_146 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_170 ∷ T_IsSuccessorSet_146 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_setoid_172 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny) → AgdaAny → T_IsSuccessorSet_146 → T_Setoid_46 Source #

du_setoid_172 ∷ T_IsSuccessorSet_146 → T_Setoid_46 Source #

d_IsMagma_178 ∷ p → p → p → p → p → () Source #

data T_IsMagma_178 Source #

Constructors

C_constructor_210 T_IsEquivalence_28 (AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny)

d_isEquivalence_186 ∷ T_IsMagma_178 → T_IsEquivalence_28 Source #

d_'8729''45'cong_188 ∷ T_IsMagma_178 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_isPartialEquivalence_192 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsMagma_178 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_192 ∷ T_IsMagma_178 → T_IsPartialEquivalence_16 Source #

d_refl_194 ∷ T_IsMagma_178 → AgdaAny → AgdaAny Source #

d_reflexive_196 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsMagma_178 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_196 ∷ T_IsMagma_178 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_sym_198 ∷ T_IsMagma_178 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_200 ∷ T_IsMagma_178 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_setoid_202 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsMagma_178 → T_Setoid_46 Source #

du_setoid_202 ∷ T_IsMagma_178 → T_Setoid_46 Source #

d_'8729''45'cong'691'_206 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsMagma_178 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_206 ∷ T_IsMagma_178 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_208 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsMagma_178 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_208 ∷ T_IsMagma_178 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_IsCommutativeMagma_214 ∷ p → p → p → p → p → () Source #

data T_IsCommutativeMagma_214 Source #

Constructors

C_constructor_248 T_IsMagma_178 (AgdaAny → AgdaAny → AgdaAny)

d_isMagma_222 ∷ T_IsCommutativeMagma_214 → T_IsMagma_178 Source #

d_comm_224 ∷ T_IsCommutativeMagma_214 → AgdaAny → AgdaAny → AgdaAny Source #

d_isEquivalence_228 ∷ T_IsCommutativeMagma_214 → T_IsEquivalence_28 Source #

d_isPartialEquivalence_230 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsCommutativeMagma_214 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_230 ∷ T_IsCommutativeMagma_214 → T_IsPartialEquivalence_16 Source #

d_refl_232 ∷ T_IsCommutativeMagma_214 → AgdaAny → AgdaAny Source #

d_reflexive_234 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsCommutativeMagma_214 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_234 ∷ T_IsCommutativeMagma_214 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_setoid_236 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsCommutativeMagma_214 → T_Setoid_46 Source #

du_setoid_236 ∷ T_IsCommutativeMagma_214 → T_Setoid_46 Source #

d_sym_238 ∷ T_IsCommutativeMagma_214 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_240 ∷ T_IsCommutativeMagma_214 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_242 ∷ T_IsCommutativeMagma_214 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_244 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsCommutativeMagma_214 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_244 ∷ T_IsCommutativeMagma_214 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_246 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsCommutativeMagma_214 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_246 ∷ T_IsCommutativeMagma_214 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_IsIdempotentMagma_252 ∷ p → p → p → p → p → () Source #

data T_IsIdempotentMagma_252 Source #

Constructors

C_constructor_286 T_IsMagma_178 (AgdaAny → AgdaAny)

d_isMagma_260 ∷ T_IsIdempotentMagma_252 → T_IsMagma_178 Source #

d_idem_262 ∷ T_IsIdempotentMagma_252 → AgdaAny → AgdaAny Source #

d_isEquivalence_266 ∷ T_IsIdempotentMagma_252 → T_IsEquivalence_28 Source #

d_isPartialEquivalence_268 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsIdempotentMagma_252 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_268 ∷ T_IsIdempotentMagma_252 → T_IsPartialEquivalence_16 Source #

d_refl_270 ∷ T_IsIdempotentMagma_252 → AgdaAny → AgdaAny Source #

d_reflexive_272 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsIdempotentMagma_252 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_272 ∷ T_IsIdempotentMagma_252 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_setoid_274 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsIdempotentMagma_252 → T_Setoid_46 Source #

du_setoid_274 ∷ T_IsIdempotentMagma_252 → T_Setoid_46 Source #

d_sym_276 ∷ T_IsIdempotentMagma_252 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_278 ∷ T_IsIdempotentMagma_252 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_280 ∷ T_IsIdempotentMagma_252 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_282 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsIdempotentMagma_252 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_282 ∷ T_IsIdempotentMagma_252 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_284 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsIdempotentMagma_252 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_284 ∷ T_IsIdempotentMagma_252 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_IsAlternativeMagma_290 ∷ p → p → p → p → p → () Source #

data T_IsAlternativeMagma_290 Source #

Constructors

C_constructor_328 T_IsMagma_178 T_Σ_14

d_isMagma_298 ∷ T_IsAlternativeMagma_290 → T_IsMagma_178 Source #

d_alter_300 ∷ T_IsAlternativeMagma_290 → T_Σ_14 Source #

d_isEquivalence_304 ∷ T_IsAlternativeMagma_290 → T_IsEquivalence_28 Source #

d_isPartialEquivalence_306 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsAlternativeMagma_290 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_306 ∷ T_IsAlternativeMagma_290 → T_IsPartialEquivalence_16 Source #

d_refl_308 ∷ T_IsAlternativeMagma_290 → AgdaAny → AgdaAny Source #

d_reflexive_310 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsAlternativeMagma_290 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_310 ∷ T_IsAlternativeMagma_290 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_setoid_312 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsAlternativeMagma_290 → T_Setoid_46 Source #

du_setoid_312 ∷ T_IsAlternativeMagma_290 → T_Setoid_46 Source #

d_sym_314 ∷ T_IsAlternativeMagma_290 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_316 ∷ T_IsAlternativeMagma_290 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_318 ∷ T_IsAlternativeMagma_290 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_320 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsAlternativeMagma_290 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_320 ∷ T_IsAlternativeMagma_290 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_322 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsAlternativeMagma_290 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_322 ∷ T_IsAlternativeMagma_290 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_alternative'737'_324 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsAlternativeMagma_290 → AgdaAny → AgdaAny → AgdaAny Source #

du_alternative'737'_324 ∷ T_IsAlternativeMagma_290 → AgdaAny → AgdaAny → AgdaAny Source #

d_alternative'691'_326 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsAlternativeMagma_290 → AgdaAny → AgdaAny → AgdaAny Source #

du_alternative'691'_326 ∷ T_IsAlternativeMagma_290 → AgdaAny → AgdaAny → AgdaAny Source #

d_IsFlexibleMagma_332 ∷ p → p → p → p → p → () Source #

data T_IsFlexibleMagma_332 Source #

Constructors

C_constructor_366 T_IsMagma_178 (AgdaAny → AgdaAny → AgdaAny)

d_isMagma_340 ∷ T_IsFlexibleMagma_332 → T_IsMagma_178 Source #

d_flex_342 ∷ T_IsFlexibleMagma_332 → AgdaAny → AgdaAny → AgdaAny Source #

d_isEquivalence_346 ∷ T_IsFlexibleMagma_332 → T_IsEquivalence_28 Source #

d_isPartialEquivalence_348 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsFlexibleMagma_332 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_348 ∷ T_IsFlexibleMagma_332 → T_IsPartialEquivalence_16 Source #

d_refl_350 ∷ T_IsFlexibleMagma_332 → AgdaAny → AgdaAny Source #

d_reflexive_352 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsFlexibleMagma_332 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_352 ∷ T_IsFlexibleMagma_332 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_setoid_354 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsFlexibleMagma_332 → T_Setoid_46 Source #

du_setoid_354 ∷ T_IsFlexibleMagma_332 → T_Setoid_46 Source #

d_sym_356 ∷ T_IsFlexibleMagma_332 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_358 ∷ T_IsFlexibleMagma_332 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_360 ∷ T_IsFlexibleMagma_332 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_362 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsFlexibleMagma_332 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_362 ∷ T_IsFlexibleMagma_332 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_364 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsFlexibleMagma_332 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_364 ∷ T_IsFlexibleMagma_332 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_IsMedialMagma_370 ∷ p → p → p → p → p → () Source #

data T_IsMedialMagma_370 Source #

Constructors

C_constructor_404 T_IsMagma_178 (AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny)

d_isMagma_378 ∷ T_IsMedialMagma_370 → T_IsMagma_178 Source #

d_medial_380 ∷ T_IsMedialMagma_370 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_isEquivalence_384 ∷ T_IsMedialMagma_370 → T_IsEquivalence_28 Source #

d_isPartialEquivalence_386 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsMedialMagma_370 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_386 ∷ T_IsMedialMagma_370 → T_IsPartialEquivalence_16 Source #

d_refl_388 ∷ T_IsMedialMagma_370 → AgdaAny → AgdaAny Source #

d_reflexive_390 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsMedialMagma_370 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_390 ∷ T_IsMedialMagma_370 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_setoid_392 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsMedialMagma_370 → T_Setoid_46 Source #

du_setoid_392 ∷ T_IsMedialMagma_370 → T_Setoid_46 Source #

d_sym_394 ∷ T_IsMedialMagma_370 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_396 ∷ T_IsMedialMagma_370 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_398 ∷ T_IsMedialMagma_370 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_400 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsMedialMagma_370 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_400 ∷ T_IsMedialMagma_370 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_402 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsMedialMagma_370 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_402 ∷ T_IsMedialMagma_370 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_IsSemimedialMagma_408 ∷ p → p → p → p → p → () Source #

data T_IsSemimedialMagma_408 Source #

Constructors

C_constructor_446 T_IsMagma_178 T_Σ_14

d_isMagma_416 ∷ T_IsSemimedialMagma_408 → T_IsMagma_178 Source #

d_semiMedial_418 ∷ T_IsSemimedialMagma_408 → T_Σ_14 Source #

d_isEquivalence_422 ∷ T_IsSemimedialMagma_408 → T_IsEquivalence_28 Source #

d_isPartialEquivalence_424 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsSemimedialMagma_408 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_424 ∷ T_IsSemimedialMagma_408 → T_IsPartialEquivalence_16 Source #

d_refl_426 ∷ T_IsSemimedialMagma_408 → AgdaAny → AgdaAny Source #

d_reflexive_428 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsSemimedialMagma_408 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_428 ∷ T_IsSemimedialMagma_408 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_setoid_430 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsSemimedialMagma_408 → T_Setoid_46 Source #

du_setoid_430 ∷ T_IsSemimedialMagma_408 → T_Setoid_46 Source #

d_sym_432 ∷ T_IsSemimedialMagma_408 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_434 ∷ T_IsSemimedialMagma_408 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_436 ∷ T_IsSemimedialMagma_408 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_438 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsSemimedialMagma_408 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_438 ∷ T_IsSemimedialMagma_408 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_440 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsSemimedialMagma_408 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_440 ∷ T_IsSemimedialMagma_408 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_semimedial'737'_442 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsSemimedialMagma_408 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_semimedial'737'_442 ∷ T_IsSemimedialMagma_408 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_semimedial'691'_444 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsSemimedialMagma_408 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_semimedial'691'_444 ∷ T_IsSemimedialMagma_408 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_IsSelectiveMagma_450 ∷ p → p → p → p → p → () Source #

data T_IsSelectiveMagma_450 Source #

Constructors

C_constructor_484 T_IsMagma_178 (AgdaAny → AgdaAny → T__'8846'__30)

d_isMagma_458 ∷ T_IsSelectiveMagma_450 → T_IsMagma_178 Source #

d_sel_460 ∷ T_IsSelectiveMagma_450 → AgdaAny → AgdaAny → T__'8846'__30 Source #

d_isEquivalence_464 ∷ T_IsSelectiveMagma_450 → T_IsEquivalence_28 Source #

d_isPartialEquivalence_466 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsSelectiveMagma_450 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_466 ∷ T_IsSelectiveMagma_450 → T_IsPartialEquivalence_16 Source #

d_refl_468 ∷ T_IsSelectiveMagma_450 → AgdaAny → AgdaAny Source #

d_reflexive_470 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsSelectiveMagma_450 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_470 ∷ T_IsSelectiveMagma_450 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_setoid_472 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsSelectiveMagma_450 → T_Setoid_46 Source #

du_setoid_472 ∷ T_IsSelectiveMagma_450 → T_Setoid_46 Source #

d_sym_474 ∷ T_IsSelectiveMagma_450 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_476 ∷ T_IsSelectiveMagma_450 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_478 ∷ T_IsSelectiveMagma_450 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_480 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsSelectiveMagma_450 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_480 ∷ T_IsSelectiveMagma_450 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_482 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsSelectiveMagma_450 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_482 ∷ T_IsSelectiveMagma_450 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_IsSemigroup_488 ∷ p → p → p → p → p → () Source #

data T_IsSemigroup_488 Source #

Constructors

C_constructor_522 T_IsMagma_178 (AgdaAny → AgdaAny → AgdaAny → AgdaAny)

d_isMagma_496 ∷ T_IsSemigroup_488 → T_IsMagma_178 Source #

d_assoc_498 ∷ T_IsSemigroup_488 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_isEquivalence_502 ∷ T_IsSemigroup_488 → T_IsEquivalence_28 Source #

d_isPartialEquivalence_504 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsSemigroup_488 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_504 ∷ T_IsSemigroup_488 → T_IsPartialEquivalence_16 Source #

d_refl_506 ∷ T_IsSemigroup_488 → AgdaAny → AgdaAny Source #

d_reflexive_508 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsSemigroup_488 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_508 ∷ T_IsSemigroup_488 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_setoid_510 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsSemigroup_488 → T_Setoid_46 Source #

du_setoid_510 ∷ T_IsSemigroup_488 → T_Setoid_46 Source #

d_sym_512 ∷ T_IsSemigroup_488 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_514 ∷ T_IsSemigroup_488 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_516 ∷ T_IsSemigroup_488 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_518 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsSemigroup_488 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_518 ∷ T_IsSemigroup_488 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_520 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsSemigroup_488 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_520 ∷ T_IsSemigroup_488 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_IsBand_526 ∷ p → p → p → p → p → () Source #

data T_IsBand_526 Source #

Constructors

C_constructor_564 T_IsSemigroup_488 (AgdaAny → AgdaAny)

d_isSemigroup_534 ∷ T_IsBand_526 → T_IsSemigroup_488 Source #

d_idem_536 ∷ T_IsBand_526 → AgdaAny → AgdaAny Source #

d_assoc_540 ∷ T_IsBand_526 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_isEquivalence_542 ∷ T_IsBand_526 → T_IsEquivalence_28 Source #

d_isMagma_544 ∷ T_IsBand_526 → T_IsMagma_178 Source #

d_isPartialEquivalence_546 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsBand_526 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_546 ∷ T_IsBand_526 → T_IsPartialEquivalence_16 Source #

d_refl_548 ∷ T_IsBand_526 → AgdaAny → AgdaAny Source #

d_reflexive_550 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsBand_526 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_550 ∷ T_IsBand_526 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_setoid_552 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsBand_526 → T_Setoid_46 Source #

du_setoid_552 ∷ T_IsBand_526 → T_Setoid_46 Source #

d_sym_554 ∷ T_IsBand_526 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_556 ∷ T_IsBand_526 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_558 ∷ T_IsBand_526 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_560 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsBand_526 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_560 ∷ T_IsBand_526 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_562 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsBand_526 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_562 ∷ T_IsBand_526 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_IsCommutativeSemigroup_568 ∷ p → p → p → p → p → () Source #

data T_IsCommutativeSemigroup_568 Source #

Constructors

C_constructor_608 T_IsSemigroup_488 (AgdaAny → AgdaAny → AgdaAny)

d_isSemigroup_576 ∷ T_IsCommutativeSemigroup_568 → T_IsSemigroup_488 Source #

d_comm_578 ∷ T_IsCommutativeSemigroup_568 → AgdaAny → AgdaAny → AgdaAny Source #

d_assoc_582 ∷ T_IsCommutativeSemigroup_568 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_isEquivalence_584 ∷ T_IsCommutativeSemigroup_568 → T_IsEquivalence_28 Source #

d_isMagma_586 ∷ T_IsCommutativeSemigroup_568 → T_IsMagma_178 Source #

d_isPartialEquivalence_588 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsCommutativeSemigroup_568 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_588 ∷ T_IsCommutativeSemigroup_568 → T_IsPartialEquivalence_16 Source #

d_refl_590 ∷ T_IsCommutativeSemigroup_568 → AgdaAny → AgdaAny Source #

d_reflexive_592 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsCommutativeSemigroup_568 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_592 ∷ T_IsCommutativeSemigroup_568 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_setoid_594 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsCommutativeSemigroup_568 → T_Setoid_46 Source #

du_setoid_594 ∷ T_IsCommutativeSemigroup_568 → T_Setoid_46 Source #

d_sym_596 ∷ T_IsCommutativeSemigroup_568 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_598 ∷ T_IsCommutativeSemigroup_568 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_600 ∷ T_IsCommutativeSemigroup_568 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_602 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsCommutativeSemigroup_568 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_602 ∷ T_IsCommutativeSemigroup_568 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_604 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsCommutativeSemigroup_568 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_604 ∷ T_IsCommutativeSemigroup_568 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_isCommutativeMagma_606 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsCommutativeSemigroup_568 → T_IsCommutativeMagma_214 Source #

du_isCommutativeMagma_606 ∷ T_IsCommutativeSemigroup_568 → T_IsCommutativeMagma_214 Source #

d_IsCommutativeBand_612 ∷ p → p → p → p → p → () Source #

data T_IsCommutativeBand_612 Source #

Constructors

C_constructor_660 T_IsBand_526 (AgdaAny → AgdaAny → AgdaAny)

d_isBand_620 ∷ T_IsCommutativeBand_612 → T_IsBand_526 Source #

d_comm_622 ∷ T_IsCommutativeBand_612 → AgdaAny → AgdaAny → AgdaAny Source #

d_assoc_626 ∷ T_IsCommutativeBand_612 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_idem_628 ∷ T_IsCommutativeBand_612 → AgdaAny → AgdaAny Source #

d_isEquivalence_630 ∷ T_IsCommutativeBand_612 → T_IsEquivalence_28 Source #

d_isMagma_632 ∷ T_IsCommutativeBand_612 → T_IsMagma_178 Source #

d_isPartialEquivalence_634 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsCommutativeBand_612 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_634 ∷ T_IsCommutativeBand_612 → T_IsPartialEquivalence_16 Source #

d_isSemigroup_636 ∷ T_IsCommutativeBand_612 → T_IsSemigroup_488 Source #

d_refl_638 ∷ T_IsCommutativeBand_612 → AgdaAny → AgdaAny Source #

d_reflexive_640 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsCommutativeBand_612 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_640 ∷ T_IsCommutativeBand_612 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_setoid_642 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsCommutativeBand_612 → T_Setoid_46 Source #

du_setoid_642 ∷ T_IsCommutativeBand_612 → T_Setoid_46 Source #

d_sym_644 ∷ T_IsCommutativeBand_612 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_646 ∷ T_IsCommutativeBand_612 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_648 ∷ T_IsCommutativeBand_612 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_650 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsCommutativeBand_612 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_650 ∷ T_IsCommutativeBand_612 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_652 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsCommutativeBand_612 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_652 ∷ T_IsCommutativeBand_612 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_isCommutativeSemigroup_654 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsCommutativeBand_612 → T_IsCommutativeSemigroup_568 Source #

du_isCommutativeSemigroup_654 ∷ T_IsCommutativeBand_612 → T_IsCommutativeSemigroup_568 Source #

d_isCommutativeMagma_658 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → T_IsCommutativeBand_612 → T_IsCommutativeMagma_214 Source #

du_isCommutativeMagma_658 ∷ T_IsCommutativeBand_612 → T_IsCommutativeMagma_214 Source #

d_IsUnitalMagma_666 ∷ p → p → p → p → p → p → () Source #

data T_IsUnitalMagma_666 Source #

Constructors

C_constructor_706 T_IsMagma_178 T_Σ_14

d_isMagma_676 ∷ T_IsUnitalMagma_666 → T_IsMagma_178 Source #

d_identity_678 ∷ T_IsUnitalMagma_666 → T_Σ_14 Source #

d_isEquivalence_682 ∷ T_IsUnitalMagma_666 → T_IsEquivalence_28 Source #

d_isPartialEquivalence_684 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsUnitalMagma_666 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_684 ∷ T_IsUnitalMagma_666 → T_IsPartialEquivalence_16 Source #

d_refl_686 ∷ T_IsUnitalMagma_666 → AgdaAny → AgdaAny Source #

d_reflexive_688 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsUnitalMagma_666 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_688 ∷ T_IsUnitalMagma_666 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_setoid_690 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsUnitalMagma_666 → T_Setoid_46 Source #

du_setoid_690 ∷ T_IsUnitalMagma_666 → T_Setoid_46 Source #

d_sym_692 ∷ T_IsUnitalMagma_666 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_694 ∷ T_IsUnitalMagma_666 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_696 ∷ T_IsUnitalMagma_666 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_698 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsUnitalMagma_666 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_698 ∷ T_IsUnitalMagma_666 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_700 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsUnitalMagma_666 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_700 ∷ T_IsUnitalMagma_666 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_identity'737'_702 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsUnitalMagma_666 → AgdaAny → AgdaAny Source #

du_identity'737'_702 ∷ T_IsUnitalMagma_666 → AgdaAny → AgdaAny Source #

d_identity'691'_704 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsUnitalMagma_666 → AgdaAny → AgdaAny Source #

du_identity'691'_704 ∷ T_IsUnitalMagma_666 → AgdaAny → AgdaAny Source #

d_IsMonoid_712 ∷ p → p → p → p → p → p → () Source #

data T_IsMonoid_712 Source #

Constructors

C_constructor_758 T_IsSemigroup_488 T_Σ_14

d_isSemigroup_722 ∷ T_IsMonoid_712 → T_IsSemigroup_488 Source #

d_identity_724 ∷ T_IsMonoid_712 → T_Σ_14 Source #

d_assoc_728 ∷ T_IsMonoid_712 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_isEquivalence_730 ∷ T_IsMonoid_712 → T_IsEquivalence_28 Source #

d_isMagma_732 ∷ T_IsMonoid_712 → T_IsMagma_178 Source #

d_isPartialEquivalence_734 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMonoid_712 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_734 ∷ T_IsMonoid_712 → T_IsPartialEquivalence_16 Source #

d_refl_736 ∷ T_IsMonoid_712 → AgdaAny → AgdaAny Source #

d_reflexive_738 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMonoid_712 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_738 ∷ T_IsMonoid_712 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_setoid_740 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMonoid_712 → T_Setoid_46 Source #

du_setoid_740 ∷ T_IsMonoid_712 → T_Setoid_46 Source #

d_sym_742 ∷ T_IsMonoid_712 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_744 ∷ T_IsMonoid_712 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_746 ∷ T_IsMonoid_712 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_748 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMonoid_712 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_748 ∷ T_IsMonoid_712 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_750 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMonoid_712 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_750 ∷ T_IsMonoid_712 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_identity'737'_752 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMonoid_712 → AgdaAny → AgdaAny Source #

du_identity'737'_752 ∷ T_IsMonoid_712 → AgdaAny → AgdaAny Source #

d_identity'691'_754 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMonoid_712 → AgdaAny → AgdaAny Source #

du_identity'691'_754 ∷ T_IsMonoid_712 → AgdaAny → AgdaAny Source #

d_isUnitalMagma_756 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMonoid_712 → T_IsUnitalMagma_666 Source #

du_isUnitalMagma_756 ∷ T_IsMonoid_712 → T_IsUnitalMagma_666 Source #

d_IsCommutativeMonoid_764 ∷ p → p → p → p → p → p → () Source #

data T_IsCommutativeMonoid_764 Source #

Constructors

C_constructor_820 T_IsMonoid_712 (AgdaAny → AgdaAny → AgdaAny)

d_isMonoid_774 ∷ T_IsCommutativeMonoid_764 → T_IsMonoid_712 Source #

d_comm_776 ∷ T_IsCommutativeMonoid_764 → AgdaAny → AgdaAny → AgdaAny Source #

d_assoc_780 ∷ T_IsCommutativeMonoid_764 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_identity_782 ∷ T_IsCommutativeMonoid_764 → T_Σ_14 Source #

d_identity'691'_784 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeMonoid_764 → AgdaAny → AgdaAny Source #

du_identity'691'_784 ∷ T_IsCommutativeMonoid_764 → AgdaAny → AgdaAny Source #

d_identity'737'_786 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeMonoid_764 → AgdaAny → AgdaAny Source #

du_identity'737'_786 ∷ T_IsCommutativeMonoid_764 → AgdaAny → AgdaAny Source #

d_isEquivalence_788 ∷ T_IsCommutativeMonoid_764 → T_IsEquivalence_28 Source #

d_isMagma_790 ∷ T_IsCommutativeMonoid_764 → T_IsMagma_178 Source #

d_isPartialEquivalence_792 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeMonoid_764 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_792 ∷ T_IsCommutativeMonoid_764 → T_IsPartialEquivalence_16 Source #

d_isSemigroup_794 ∷ T_IsCommutativeMonoid_764 → T_IsSemigroup_488 Source #

d_isUnitalMagma_796 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeMonoid_764 → T_IsUnitalMagma_666 Source #

du_isUnitalMagma_796 ∷ T_IsCommutativeMonoid_764 → T_IsUnitalMagma_666 Source #

d_refl_798 ∷ T_IsCommutativeMonoid_764 → AgdaAny → AgdaAny Source #

d_reflexive_800 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeMonoid_764 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_800 ∷ T_IsCommutativeMonoid_764 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_setoid_802 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeMonoid_764 → T_Setoid_46 Source #

du_setoid_802 ∷ T_IsCommutativeMonoid_764 → T_Setoid_46 Source #

d_sym_804 ∷ T_IsCommutativeMonoid_764 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_806 ∷ T_IsCommutativeMonoid_764 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_808 ∷ T_IsCommutativeMonoid_764 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_810 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeMonoid_764 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_810 ∷ T_IsCommutativeMonoid_764 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_812 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeMonoid_764 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_812 ∷ T_IsCommutativeMonoid_764 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_isCommutativeSemigroup_814 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeMonoid_764 → T_IsCommutativeSemigroup_568 Source #

du_isCommutativeSemigroup_814 ∷ T_IsCommutativeMonoid_764 → T_IsCommutativeSemigroup_568 Source #

d_isCommutativeMagma_818 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeMonoid_764 → T_IsCommutativeMagma_214 Source #

du_isCommutativeMagma_818 ∷ T_IsCommutativeMonoid_764 → T_IsCommutativeMagma_214 Source #

d_IsIdempotentMonoid_826 ∷ p → p → p → p → p → p → () Source #

data T_IsIdempotentMonoid_826 Source #

Constructors

C_constructor_878 T_IsMonoid_712 (AgdaAny → AgdaAny)

d_isMonoid_836 ∷ T_IsIdempotentMonoid_826 → T_IsMonoid_712 Source #

d_idem_838 ∷ T_IsIdempotentMonoid_826 → AgdaAny → AgdaAny Source #

d_assoc_842 ∷ T_IsIdempotentMonoid_826 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_identity_844 ∷ T_IsIdempotentMonoid_826 → T_Σ_14 Source #

d_identity'691'_846 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsIdempotentMonoid_826 → AgdaAny → AgdaAny Source #

du_identity'691'_846 ∷ T_IsIdempotentMonoid_826 → AgdaAny → AgdaAny Source #

d_identity'737'_848 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsIdempotentMonoid_826 → AgdaAny → AgdaAny Source #

du_identity'737'_848 ∷ T_IsIdempotentMonoid_826 → AgdaAny → AgdaAny Source #

d_isEquivalence_850 ∷ T_IsIdempotentMonoid_826 → T_IsEquivalence_28 Source #

d_isMagma_852 ∷ T_IsIdempotentMonoid_826 → T_IsMagma_178 Source #

d_isPartialEquivalence_854 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsIdempotentMonoid_826 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_854 ∷ T_IsIdempotentMonoid_826 → T_IsPartialEquivalence_16 Source #

d_isSemigroup_856 ∷ T_IsIdempotentMonoid_826 → T_IsSemigroup_488 Source #

d_isUnitalMagma_858 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsIdempotentMonoid_826 → T_IsUnitalMagma_666 Source #

du_isUnitalMagma_858 ∷ T_IsIdempotentMonoid_826 → T_IsUnitalMagma_666 Source #

d_refl_860 ∷ T_IsIdempotentMonoid_826 → AgdaAny → AgdaAny Source #

d_reflexive_862 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsIdempotentMonoid_826 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_862 ∷ T_IsIdempotentMonoid_826 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_setoid_864 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsIdempotentMonoid_826 → T_Setoid_46 Source #

du_setoid_864 ∷ T_IsIdempotentMonoid_826 → T_Setoid_46 Source #

d_sym_866 ∷ T_IsIdempotentMonoid_826 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_868 ∷ T_IsIdempotentMonoid_826 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_870 ∷ T_IsIdempotentMonoid_826 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_872 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsIdempotentMonoid_826 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_872 ∷ T_IsIdempotentMonoid_826 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_874 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsIdempotentMonoid_826 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_874 ∷ T_IsIdempotentMonoid_826 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_isBand_876 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsIdempotentMonoid_826 → T_IsBand_526 Source #

du_isBand_876 ∷ T_IsIdempotentMonoid_826 → T_IsBand_526 Source #

d_IsIdempotentCommutativeMonoid_884 ∷ p → p → p → p → p → p → () Source #

data T_IsIdempotentCommutativeMonoid_884 Source #

Constructors

C_constructor_950 T_IsCommutativeMonoid_764 (AgdaAny → AgdaAny)

d_isCommutativeMonoid_894 ∷ T_IsIdempotentCommutativeMonoid_884 → T_IsCommutativeMonoid_764 Source #

d_idem_896 ∷ T_IsIdempotentCommutativeMonoid_884 → AgdaAny → AgdaAny Source #

d_assoc_900 ∷ T_IsIdempotentCommutativeMonoid_884 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_comm_902 ∷ T_IsIdempotentCommutativeMonoid_884 → AgdaAny → AgdaAny → AgdaAny Source #

d_identity_904 ∷ T_IsIdempotentCommutativeMonoid_884 → T_Σ_14 Source #

d_identity'691'_906 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsIdempotentCommutativeMonoid_884 → AgdaAny → AgdaAny Source #

du_identity'691'_906 ∷ T_IsIdempotentCommutativeMonoid_884 → AgdaAny → AgdaAny Source #

d_identity'737'_908 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsIdempotentCommutativeMonoid_884 → AgdaAny → AgdaAny Source #

du_identity'737'_908 ∷ T_IsIdempotentCommutativeMonoid_884 → AgdaAny → AgdaAny Source #

d_isCommutativeMagma_910 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsIdempotentCommutativeMonoid_884 → T_IsCommutativeMagma_214 Source #

du_isCommutativeMagma_910 ∷ T_IsIdempotentCommutativeMonoid_884 → T_IsCommutativeMagma_214 Source #

d_isCommutativeSemigroup_912 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsIdempotentCommutativeMonoid_884 → T_IsCommutativeSemigroup_568 Source #

du_isCommutativeSemigroup_912 ∷ T_IsIdempotentCommutativeMonoid_884 → T_IsCommutativeSemigroup_568 Source #

d_isEquivalence_914 ∷ T_IsIdempotentCommutativeMonoid_884 → T_IsEquivalence_28 Source #

d_isMagma_916 ∷ T_IsIdempotentCommutativeMonoid_884 → T_IsMagma_178 Source #

d_isMonoid_918 ∷ T_IsIdempotentCommutativeMonoid_884 → T_IsMonoid_712 Source #

d_isPartialEquivalence_920 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsIdempotentCommutativeMonoid_884 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_920 ∷ T_IsIdempotentCommutativeMonoid_884 → T_IsPartialEquivalence_16 Source #

d_isSemigroup_922 ∷ T_IsIdempotentCommutativeMonoid_884 → T_IsSemigroup_488 Source #

d_isUnitalMagma_924 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsIdempotentCommutativeMonoid_884 → T_IsUnitalMagma_666 Source #

du_isUnitalMagma_924 ∷ T_IsIdempotentCommutativeMonoid_884 → T_IsUnitalMagma_666 Source #

d_refl_926 ∷ T_IsIdempotentCommutativeMonoid_884 → AgdaAny → AgdaAny Source #

d_reflexive_928 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsIdempotentCommutativeMonoid_884 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_928 ∷ T_IsIdempotentCommutativeMonoid_884 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_setoid_930 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsIdempotentCommutativeMonoid_884 → T_Setoid_46 Source #

du_setoid_930 ∷ T_IsIdempotentCommutativeMonoid_884 → T_Setoid_46 Source #

d_sym_932 ∷ T_IsIdempotentCommutativeMonoid_884 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_934 ∷ T_IsIdempotentCommutativeMonoid_884 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_936 ∷ T_IsIdempotentCommutativeMonoid_884 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_938 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsIdempotentCommutativeMonoid_884 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_938 ∷ T_IsIdempotentCommutativeMonoid_884 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_940 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsIdempotentCommutativeMonoid_884 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_940 ∷ T_IsIdempotentCommutativeMonoid_884 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_isIdempotentMonoid_942 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsIdempotentCommutativeMonoid_884 → T_IsIdempotentMonoid_826 Source #

du_isIdempotentMonoid_942 ∷ T_IsIdempotentCommutativeMonoid_884 → T_IsIdempotentMonoid_826 Source #

d_isBand_946 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsIdempotentCommutativeMonoid_884 → T_IsBand_526 Source #

du_isBand_946 ∷ T_IsIdempotentCommutativeMonoid_884 → T_IsBand_526 Source #

d_isCommutativeBand_948 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsIdempotentCommutativeMonoid_884 → T_IsCommutativeBand_612 Source #

du_isCommutativeBand_948 ∷ T_IsIdempotentCommutativeMonoid_884 → T_IsCommutativeBand_612 Source #

d_IsInvertibleMagma_958 ∷ p → p → p → p → p → p → p → () Source #

data T_IsInvertibleMagma_958 Source #

Constructors

C_constructor_1004 T_IsMagma_178 T_Σ_14 (AgdaAny → AgdaAny → AgdaAny → AgdaAny)

d_isMagma_972 ∷ T_IsInvertibleMagma_958 → T_IsMagma_178 Source #

d_inverse_974 ∷ T_IsInvertibleMagma_958 → T_Σ_14 Source #

d_'8315''185''45'cong_976 ∷ T_IsInvertibleMagma_958 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_isEquivalence_980 ∷ T_IsInvertibleMagma_958 → T_IsEquivalence_28 Source #

d_isPartialEquivalence_982 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsInvertibleMagma_958 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_982 ∷ T_IsInvertibleMagma_958 → T_IsPartialEquivalence_16 Source #

d_refl_984 ∷ T_IsInvertibleMagma_958 → AgdaAny → AgdaAny Source #

d_reflexive_986 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsInvertibleMagma_958 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_986 ∷ T_IsInvertibleMagma_958 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_setoid_988 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsInvertibleMagma_958 → T_Setoid_46 Source #

du_setoid_988 ∷ T_IsInvertibleMagma_958 → T_Setoid_46 Source #

d_sym_990 ∷ T_IsInvertibleMagma_958 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_992 ∷ T_IsInvertibleMagma_958 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_994 ∷ T_IsInvertibleMagma_958 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_996 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsInvertibleMagma_958 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_996 ∷ T_IsInvertibleMagma_958 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_998 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsInvertibleMagma_958 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_998 ∷ T_IsInvertibleMagma_958 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_inverse'737'_1000 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsInvertibleMagma_958 → AgdaAny → AgdaAny Source #

du_inverse'737'_1000 ∷ T_IsInvertibleMagma_958 → AgdaAny → AgdaAny Source #

d_inverse'691'_1002 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsInvertibleMagma_958 → AgdaAny → AgdaAny Source #

du_inverse'691'_1002 ∷ T_IsInvertibleMagma_958 → AgdaAny → AgdaAny Source #

d_IsInvertibleUnitalMagma_1012 ∷ p → p → p → p → p → p → p → () Source #

data T_IsInvertibleUnitalMagma_1012 Source #

Constructors

C_constructor_1066 T_IsInvertibleMagma_958 T_Σ_14

d_isInvertibleMagma_1024 ∷ T_IsInvertibleUnitalMagma_1012 → T_IsInvertibleMagma_958 Source #

d_identity_1026 ∷ T_IsInvertibleUnitalMagma_1012 → T_Σ_14 Source #

d_inverse_1030 ∷ T_IsInvertibleUnitalMagma_1012 → T_Σ_14 Source #

d_inverse'691'_1032 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsInvertibleUnitalMagma_1012 → AgdaAny → AgdaAny Source #

du_inverse'691'_1032 ∷ T_IsInvertibleUnitalMagma_1012 → AgdaAny → AgdaAny Source #

d_inverse'737'_1034 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsInvertibleUnitalMagma_1012 → AgdaAny → AgdaAny Source #

du_inverse'737'_1034 ∷ T_IsInvertibleUnitalMagma_1012 → AgdaAny → AgdaAny Source #

d_isEquivalence_1036 ∷ T_IsInvertibleUnitalMagma_1012 → T_IsEquivalence_28 Source #

d_isMagma_1038 ∷ T_IsInvertibleUnitalMagma_1012 → T_IsMagma_178 Source #

d_isPartialEquivalence_1040 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsInvertibleUnitalMagma_1012 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_1040 ∷ T_IsInvertibleUnitalMagma_1012 → T_IsPartialEquivalence_16 Source #

d_refl_1042 ∷ T_IsInvertibleUnitalMagma_1012 → AgdaAny → AgdaAny Source #

d_reflexive_1044 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsInvertibleUnitalMagma_1012 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_1044 ∷ T_IsInvertibleUnitalMagma_1012 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_setoid_1046 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsInvertibleUnitalMagma_1012 → T_Setoid_46 Source #

du_setoid_1046 ∷ T_IsInvertibleUnitalMagma_1012 → T_Setoid_46 Source #

d_sym_1048 ∷ T_IsInvertibleUnitalMagma_1012 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_1050 ∷ T_IsInvertibleUnitalMagma_1012 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8315''185''45'cong_1052 ∷ T_IsInvertibleUnitalMagma_1012 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_1054 ∷ T_IsInvertibleUnitalMagma_1012 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_1056 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsInvertibleUnitalMagma_1012 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_1056 ∷ T_IsInvertibleUnitalMagma_1012 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_1058 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsInvertibleUnitalMagma_1012 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_1058 ∷ T_IsInvertibleUnitalMagma_1012 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_identity'737'_1060 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsInvertibleUnitalMagma_1012 → AgdaAny → AgdaAny Source #

du_identity'737'_1060 ∷ T_IsInvertibleUnitalMagma_1012 → AgdaAny → AgdaAny Source #

d_identity'691'_1062 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsInvertibleUnitalMagma_1012 → AgdaAny → AgdaAny Source #

du_identity'691'_1062 ∷ T_IsInvertibleUnitalMagma_1012 → AgdaAny → AgdaAny Source #

d_isUnitalMagma_1064 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsInvertibleUnitalMagma_1012 → T_IsUnitalMagma_666 Source #

du_isUnitalMagma_1064 ∷ T_IsInvertibleUnitalMagma_1012 → T_IsUnitalMagma_666 Source #

d_IsGroup_1074 ∷ p → p → p → p → p → p → p → () Source #

data T_IsGroup_1074 Source #

Constructors

C_constructor_1164 T_IsMonoid_712 T_Σ_14 (AgdaAny → AgdaAny → AgdaAny → AgdaAny)

d_isMonoid_1088 ∷ T_IsGroup_1074 → T_IsMonoid_712 Source #

d_inverse_1090 ∷ T_IsGroup_1074 → T_Σ_14 Source #

d_'8315''185''45'cong_1092 ∷ T_IsGroup_1074 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_assoc_1096 ∷ T_IsGroup_1074 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_identity_1098 ∷ T_IsGroup_1074 → T_Σ_14 Source #

d_identity'691'_1100 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsGroup_1074 → AgdaAny → AgdaAny Source #

du_identity'691'_1100 ∷ T_IsGroup_1074 → AgdaAny → AgdaAny Source #

d_identity'737'_1102 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsGroup_1074 → AgdaAny → AgdaAny Source #

du_identity'737'_1102 ∷ T_IsGroup_1074 → AgdaAny → AgdaAny Source #

d_isEquivalence_1104 ∷ T_IsGroup_1074 → T_IsEquivalence_28 Source #

d_isMagma_1106 ∷ T_IsGroup_1074 → T_IsMagma_178 Source #

d_isPartialEquivalence_1108 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsGroup_1074 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_1108 ∷ T_IsGroup_1074 → T_IsPartialEquivalence_16 Source #

d_isSemigroup_1110 ∷ T_IsGroup_1074 → T_IsSemigroup_488 Source #

d_isUnitalMagma_1112 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsGroup_1074 → T_IsUnitalMagma_666 Source #

du_isUnitalMagma_1112 ∷ T_IsGroup_1074 → T_IsUnitalMagma_666 Source #

d_refl_1114 ∷ T_IsGroup_1074 → AgdaAny → AgdaAny Source #

d_reflexive_1116 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsGroup_1074 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_1116 ∷ T_IsGroup_1074 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_setoid_1118 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsGroup_1074 → T_Setoid_46 Source #

du_setoid_1118 ∷ T_IsGroup_1074 → T_Setoid_46 Source #

d_sym_1120 ∷ T_IsGroup_1074 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_1122 ∷ T_IsGroup_1074 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_1124 ∷ T_IsGroup_1074 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_1126 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsGroup_1074 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_1126 ∷ T_IsGroup_1074 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_1128 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsGroup_1074 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_1128 ∷ T_IsGroup_1074 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d__'92''92'__1130 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsGroup_1074 → AgdaAny → AgdaAny → AgdaAny Source #

du__'92''92'__1130 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → AgdaAny Source #

d__'47''47'__1136 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsGroup_1074 → AgdaAny → AgdaAny → AgdaAny Source #

du__'47''47'__1136 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → AgdaAny Source #

d__'45'__1142 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsGroup_1074 → AgdaAny → AgdaAny → AgdaAny Source #

du__'45'__1142 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → AgdaAny Source #

d_inverse'737'_1144 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsGroup_1074 → AgdaAny → AgdaAny Source #

du_inverse'737'_1144 ∷ T_IsGroup_1074 → AgdaAny → AgdaAny Source #

d_inverse'691'_1146 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsGroup_1074 → AgdaAny → AgdaAny Source #

du_inverse'691'_1146 ∷ T_IsGroup_1074 → AgdaAny → AgdaAny Source #

d_unique'737''45''8315''185'_1152 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsGroup_1074 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_unique'737''45''8315''185'_1152 ∷ (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsGroup_1074 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_unique'691''45''8315''185'_1158 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsGroup_1074 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_unique'691''45''8315''185'_1158 ∷ (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsGroup_1074 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_isInvertibleMagma_1160 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsGroup_1074 → T_IsInvertibleMagma_958 Source #

du_isInvertibleMagma_1160 ∷ T_IsGroup_1074 → T_IsInvertibleMagma_958 Source #

d_isInvertibleUnitalMagma_1162 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsGroup_1074 → T_IsInvertibleUnitalMagma_1012 Source #

du_isInvertibleUnitalMagma_1162 ∷ T_IsGroup_1074 → T_IsInvertibleUnitalMagma_1012 Source #

d_IsAbelianGroup_1172 ∷ p → p → p → p → p → p → p → () Source #

data T_IsAbelianGroup_1172 Source #

Constructors

C_constructor_1252 T_IsGroup_1074 (AgdaAny → AgdaAny → AgdaAny)

d_isGroup_1184 ∷ T_IsAbelianGroup_1172 → T_IsGroup_1074 Source #

d_comm_1186 ∷ T_IsAbelianGroup_1172 → AgdaAny → AgdaAny → AgdaAny Source #

d__'47''47'__1190 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsAbelianGroup_1172 → AgdaAny → AgdaAny → AgdaAny Source #

du__'47''47'__1190 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → AgdaAny Source #

d_assoc_1192 ∷ T_IsAbelianGroup_1172 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_identity_1194 ∷ T_IsAbelianGroup_1172 → T_Σ_14 Source #

d_identity'691'_1196 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsAbelianGroup_1172 → AgdaAny → AgdaAny Source #

du_identity'691'_1196 ∷ T_IsAbelianGroup_1172 → AgdaAny → AgdaAny Source #

d_identity'737'_1198 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsAbelianGroup_1172 → AgdaAny → AgdaAny Source #

du_identity'737'_1198 ∷ T_IsAbelianGroup_1172 → AgdaAny → AgdaAny Source #

d_inverse_1200 ∷ T_IsAbelianGroup_1172 → T_Σ_14 Source #

d_inverse'691'_1202 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsAbelianGroup_1172 → AgdaAny → AgdaAny Source #

du_inverse'691'_1202 ∷ T_IsAbelianGroup_1172 → AgdaAny → AgdaAny Source #

d_inverse'737'_1204 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsAbelianGroup_1172 → AgdaAny → AgdaAny Source #

du_inverse'737'_1204 ∷ T_IsAbelianGroup_1172 → AgdaAny → AgdaAny Source #

d_isEquivalence_1206 ∷ T_IsAbelianGroup_1172 → T_IsEquivalence_28 Source #

d_isInvertibleMagma_1208 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsAbelianGroup_1172 → T_IsInvertibleMagma_958 Source #

du_isInvertibleMagma_1208 ∷ T_IsAbelianGroup_1172 → T_IsInvertibleMagma_958 Source #

d_isInvertibleUnitalMagma_1210 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsAbelianGroup_1172 → T_IsInvertibleUnitalMagma_1012 Source #

du_isInvertibleUnitalMagma_1210 ∷ T_IsAbelianGroup_1172 → T_IsInvertibleUnitalMagma_1012 Source #

d_isMagma_1212 ∷ T_IsAbelianGroup_1172 → T_IsMagma_178 Source #

d_isMonoid_1214 ∷ T_IsAbelianGroup_1172 → T_IsMonoid_712 Source #

d_isPartialEquivalence_1216 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsAbelianGroup_1172 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_1216 ∷ T_IsAbelianGroup_1172 → T_IsPartialEquivalence_16 Source #

d_isSemigroup_1218 ∷ T_IsAbelianGroup_1172 → T_IsSemigroup_488 Source #

d_isUnitalMagma_1220 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsAbelianGroup_1172 → T_IsUnitalMagma_666 Source #

du_isUnitalMagma_1220 ∷ T_IsAbelianGroup_1172 → T_IsUnitalMagma_666 Source #

d_refl_1222 ∷ T_IsAbelianGroup_1172 → AgdaAny → AgdaAny Source #

d_reflexive_1224 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsAbelianGroup_1172 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_1224 ∷ T_IsAbelianGroup_1172 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_setoid_1226 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsAbelianGroup_1172 → T_Setoid_46 Source #

du_setoid_1226 ∷ T_IsAbelianGroup_1172 → T_Setoid_46 Source #

d_sym_1228 ∷ T_IsAbelianGroup_1172 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_1230 ∷ T_IsAbelianGroup_1172 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_unique'691''45''8315''185'_1232 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsAbelianGroup_1172 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_unique'691''45''8315''185'_1232 ∷ (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsAbelianGroup_1172 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_unique'737''45''8315''185'_1234 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsAbelianGroup_1172 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_unique'737''45''8315''185'_1234 ∷ (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsAbelianGroup_1172 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8315''185''45'cong_1236 ∷ T_IsAbelianGroup_1172 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_1238 ∷ T_IsAbelianGroup_1172 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_1240 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsAbelianGroup_1172 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_1240 ∷ T_IsAbelianGroup_1172 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_1242 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsAbelianGroup_1172 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_1242 ∷ T_IsAbelianGroup_1172 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_isCommutativeMonoid_1244 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsAbelianGroup_1172 → T_IsCommutativeMonoid_764 Source #

du_isCommutativeMonoid_1244 ∷ T_IsAbelianGroup_1172 → T_IsCommutativeMonoid_764 Source #

d_isCommutativeMagma_1248 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsAbelianGroup_1172 → T_IsCommutativeMagma_214 Source #

du_isCommutativeMagma_1248 ∷ T_IsAbelianGroup_1172 → T_IsCommutativeMagma_214 Source #

d_isCommutativeSemigroup_1250 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsAbelianGroup_1172 → T_IsCommutativeSemigroup_568 Source #

du_isCommutativeSemigroup_1250 ∷ T_IsAbelianGroup_1172 → T_IsCommutativeSemigroup_568 Source #

d_IsNearSemiring_1260 ∷ p → p → p → p → p → p → p → () Source #

data T_IsNearSemiring_1260 Source #

Constructors

C_constructor_1334 T_IsMonoid_712 (AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny) (AgdaAny → AgdaAny → AgdaAny → AgdaAny) (AgdaAny → AgdaAny → AgdaAny → AgdaAny) (AgdaAny → AgdaAny)

d_'43''45'isMonoid_1278 ∷ T_IsNearSemiring_1260 → T_IsMonoid_712 Source #

d_'42''45'cong_1280 ∷ T_IsNearSemiring_1260 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'42''45'assoc_1282 ∷ T_IsNearSemiring_1260 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_distrib'691'_1284 ∷ T_IsNearSemiring_1260 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_zero'737'_1286 ∷ T_IsNearSemiring_1260 → AgdaAny → AgdaAny Source #

d_assoc_1290 ∷ T_IsNearSemiring_1260 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_1292 ∷ T_IsNearSemiring_1260 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_1294 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsNearSemiring_1260 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_1294 ∷ T_IsNearSemiring_1260 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_1296 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsNearSemiring_1260 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_1296 ∷ T_IsNearSemiring_1260 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_identity_1298 ∷ T_IsNearSemiring_1260 → T_Σ_14 Source #

d_identity'691'_1300 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsNearSemiring_1260 → AgdaAny → AgdaAny Source #

du_identity'691'_1300 ∷ T_IsNearSemiring_1260 → AgdaAny → AgdaAny Source #

d_identity'737'_1302 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsNearSemiring_1260 → AgdaAny → AgdaAny Source #

du_identity'737'_1302 ∷ T_IsNearSemiring_1260 → AgdaAny → AgdaAny Source #

d_isMagma_1304 ∷ T_IsNearSemiring_1260 → T_IsMagma_178 Source #

d_isSemigroup_1306 ∷ T_IsNearSemiring_1260 → T_IsSemigroup_488 Source #

d_isUnitalMagma_1308 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsNearSemiring_1260 → T_IsUnitalMagma_666 Source #

du_isUnitalMagma_1308 ∷ T_IsNearSemiring_1260 → T_IsUnitalMagma_666 Source #

d_isEquivalence_1310 ∷ T_IsNearSemiring_1260 → T_IsEquivalence_28 Source #

d_isPartialEquivalence_1312 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsNearSemiring_1260 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_1312 ∷ T_IsNearSemiring_1260 → T_IsPartialEquivalence_16 Source #

d_refl_1314 ∷ T_IsNearSemiring_1260 → AgdaAny → AgdaAny Source #

d_reflexive_1316 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsNearSemiring_1260 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_1316 ∷ T_IsNearSemiring_1260 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_setoid_1318 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsNearSemiring_1260 → T_Setoid_46 Source #

du_setoid_1318 ∷ T_IsNearSemiring_1260 → T_Setoid_46 Source #

d_sym_1320 ∷ T_IsNearSemiring_1260 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_1322 ∷ T_IsNearSemiring_1260 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'42''45'isMagma_1324 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsNearSemiring_1260 → T_IsMagma_178 Source #

du_'42''45'isMagma_1324 ∷ T_IsNearSemiring_1260 → T_IsMagma_178 Source #

d_'42''45'isSemigroup_1326 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsNearSemiring_1260 → T_IsSemigroup_488 Source #

du_'42''45'isSemigroup_1326 ∷ T_IsNearSemiring_1260 → T_IsSemigroup_488 Source #

d_'8729''45'cong'691'_1330 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsNearSemiring_1260 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_1330 ∷ T_IsNearSemiring_1260 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_1332 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsNearSemiring_1260 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_1332 ∷ T_IsNearSemiring_1260 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_IsSemiringWithoutOne_1342 ∷ p → p → p → p → p → p → p → () Source #

data T_IsSemiringWithoutOne_1342 Source #

Constructors

C_constructor_1430 T_IsCommutativeMonoid_764 (AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny) (AgdaAny → AgdaAny → AgdaAny → AgdaAny) T_Σ_14 T_Σ_14

d_'43''45'isCommutativeMonoid_1360 ∷ T_IsSemiringWithoutOne_1342 → T_IsCommutativeMonoid_764 Source #

d_'42''45'cong_1362 ∷ T_IsSemiringWithoutOne_1342 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'42''45'assoc_1364 ∷ T_IsSemiringWithoutOne_1342 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_distrib_1366 ∷ T_IsSemiringWithoutOne_1342 → T_Σ_14 Source #

d_zero_1368 ∷ T_IsSemiringWithoutOne_1342 → T_Σ_14 Source #

d_assoc_1372 ∷ T_IsSemiringWithoutOne_1342 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_comm_1374 ∷ T_IsSemiringWithoutOne_1342 → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_1376 ∷ T_IsSemiringWithoutOne_1342 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_1378 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsSemiringWithoutOne_1342 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_1378 ∷ T_IsSemiringWithoutOne_1342 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_1380 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsSemiringWithoutOne_1342 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_1380 ∷ T_IsSemiringWithoutOne_1342 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_identity_1382 ∷ T_IsSemiringWithoutOne_1342 → T_Σ_14 Source #

d_identity'691'_1384 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsSemiringWithoutOne_1342 → AgdaAny → AgdaAny Source #

du_identity'691'_1384 ∷ T_IsSemiringWithoutOne_1342 → AgdaAny → AgdaAny Source #

d_identity'737'_1386 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsSemiringWithoutOne_1342 → AgdaAny → AgdaAny Source #

du_identity'737'_1386 ∷ T_IsSemiringWithoutOne_1342 → AgdaAny → AgdaAny Source #

d_isCommutativeMagma_1388 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsSemiringWithoutOne_1342 → T_IsCommutativeMagma_214 Source #

du_isCommutativeMagma_1388 ∷ T_IsSemiringWithoutOne_1342 → T_IsCommutativeMagma_214 Source #

d_isCommutativeSemigroup_1390 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsSemiringWithoutOne_1342 → T_IsCommutativeSemigroup_568 Source #

du_isCommutativeSemigroup_1390 ∷ T_IsSemiringWithoutOne_1342 → T_IsCommutativeSemigroup_568 Source #

d_isMonoid_1392 ∷ T_IsSemiringWithoutOne_1342 → T_IsMonoid_712 Source #

d_isEquivalence_1394 ∷ T_IsSemiringWithoutOne_1342 → T_IsEquivalence_28 Source #

d_setoid_1396 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsSemiringWithoutOne_1342 → T_Setoid_46 Source #

du_setoid_1396 ∷ T_IsSemiringWithoutOne_1342 → T_Setoid_46 Source #

d_isPartialEquivalence_1400 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsSemiringWithoutOne_1342 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_1400 ∷ T_IsSemiringWithoutOne_1342 → T_IsPartialEquivalence_16 Source #

d_refl_1402 ∷ T_IsSemiringWithoutOne_1342 → AgdaAny → AgdaAny Source #

d_reflexive_1404 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsSemiringWithoutOne_1342 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_1404 ∷ T_IsSemiringWithoutOne_1342 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_sym_1406 ∷ T_IsSemiringWithoutOne_1342 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_1408 ∷ T_IsSemiringWithoutOne_1342 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'42''45'isMagma_1410 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsSemiringWithoutOne_1342 → T_IsMagma_178 Source #

du_'42''45'isMagma_1410 ∷ T_IsSemiringWithoutOne_1342 → T_IsMagma_178 Source #

d_'42''45'isSemigroup_1412 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsSemiringWithoutOne_1342 → T_IsSemigroup_488 Source #

du_'42''45'isSemigroup_1412 ∷ T_IsSemiringWithoutOne_1342 → T_IsSemigroup_488 Source #

d_'8729''45'cong'691'_1416 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsSemiringWithoutOne_1342 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_1416 ∷ T_IsSemiringWithoutOne_1342 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_1418 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsSemiringWithoutOne_1342 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_1418 ∷ T_IsSemiringWithoutOne_1342 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_distrib'737'_1420 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsSemiringWithoutOne_1342 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_distrib'737'_1420 ∷ T_IsSemiringWithoutOne_1342 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_distrib'691'_1422 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsSemiringWithoutOne_1342 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_distrib'691'_1422 ∷ T_IsSemiringWithoutOne_1342 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_zero'737'_1424 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsSemiringWithoutOne_1342 → AgdaAny → AgdaAny Source #

du_zero'737'_1424 ∷ T_IsSemiringWithoutOne_1342 → AgdaAny → AgdaAny Source #

d_zero'691'_1426 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsSemiringWithoutOne_1342 → AgdaAny → AgdaAny Source #

du_zero'691'_1426 ∷ T_IsSemiringWithoutOne_1342 → AgdaAny → AgdaAny Source #

d_isNearSemiring_1428 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsSemiringWithoutOne_1342 → T_IsNearSemiring_1260 Source #

du_isNearSemiring_1428 ∷ T_IsSemiringWithoutOne_1342 → T_IsNearSemiring_1260 Source #

d_IsCommutativeSemiringWithoutOne_1438 ∷ p → p → p → p → p → p → p → () Source #

data T_IsCommutativeSemiringWithoutOne_1438 Source #

Constructors

C_constructor_1526 T_IsSemiringWithoutOne_1342 (AgdaAny → AgdaAny → AgdaAny)

d_isSemiringWithoutOne_1450 ∷ T_IsCommutativeSemiringWithoutOne_1438 → T_IsSemiringWithoutOne_1342 Source #

d_'42''45'comm_1452 ∷ T_IsCommutativeSemiringWithoutOne_1438 → AgdaAny → AgdaAny → AgdaAny Source #

d_'42''45'assoc_1456 ∷ T_IsCommutativeSemiringWithoutOne_1438 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'42''45'cong_1458 ∷ T_IsCommutativeSemiringWithoutOne_1438 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_1460 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeSemiringWithoutOne_1438 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_1460 ∷ T_IsCommutativeSemiringWithoutOne_1438 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_1462 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeSemiringWithoutOne_1438 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_1462 ∷ T_IsCommutativeSemiringWithoutOne_1438 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'42''45'isMagma_1464 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeSemiringWithoutOne_1438 → T_IsMagma_178 Source #

du_'42''45'isMagma_1464 ∷ T_IsCommutativeSemiringWithoutOne_1438 → T_IsMagma_178 Source #

d_'42''45'isSemigroup_1466 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeSemiringWithoutOne_1438 → T_IsSemigroup_488 Source #

du_'42''45'isSemigroup_1466 ∷ T_IsCommutativeSemiringWithoutOne_1438 → T_IsSemigroup_488 Source #

d_assoc_1468 ∷ T_IsCommutativeSemiringWithoutOne_1438 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_comm_1470 ∷ T_IsCommutativeSemiringWithoutOne_1438 → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_1472 ∷ T_IsCommutativeSemiringWithoutOne_1438 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_1474 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeSemiringWithoutOne_1438 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_1474 ∷ T_IsCommutativeSemiringWithoutOne_1438 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_1476 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeSemiringWithoutOne_1438 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_1476 ∷ T_IsCommutativeSemiringWithoutOne_1438 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_identity_1478 ∷ T_IsCommutativeSemiringWithoutOne_1438 → T_Σ_14 Source #

d_identity'691'_1480 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeSemiringWithoutOne_1438 → AgdaAny → AgdaAny Source #

du_identity'691'_1480 ∷ T_IsCommutativeSemiringWithoutOne_1438 → AgdaAny → AgdaAny Source #

d_identity'737'_1482 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeSemiringWithoutOne_1438 → AgdaAny → AgdaAny Source #

du_identity'737'_1482 ∷ T_IsCommutativeSemiringWithoutOne_1438 → AgdaAny → AgdaAny Source #

d_isCommutativeMagma_1484 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeSemiringWithoutOne_1438 → T_IsCommutativeMagma_214 Source #

du_isCommutativeMagma_1484 ∷ T_IsCommutativeSemiringWithoutOne_1438 → T_IsCommutativeMagma_214 Source #

d_'43''45'isCommutativeMonoid_1486 ∷ T_IsCommutativeSemiringWithoutOne_1438 → T_IsCommutativeMonoid_764 Source #

d_isCommutativeSemigroup_1488 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeSemiringWithoutOne_1438 → T_IsCommutativeSemigroup_568 Source #

du_isCommutativeSemigroup_1488 ∷ T_IsCommutativeSemiringWithoutOne_1438 → T_IsCommutativeSemigroup_568 Source #

d_isMonoid_1490 ∷ T_IsCommutativeSemiringWithoutOne_1438 → T_IsMonoid_712 Source #

d_distrib_1492 ∷ T_IsCommutativeSemiringWithoutOne_1438 → T_Σ_14 Source #

d_distrib'691'_1494 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeSemiringWithoutOne_1438 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_distrib'691'_1494 ∷ T_IsCommutativeSemiringWithoutOne_1438 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_distrib'737'_1496 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeSemiringWithoutOne_1438 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_distrib'737'_1496 ∷ T_IsCommutativeSemiringWithoutOne_1438 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_isEquivalence_1498 ∷ T_IsCommutativeSemiringWithoutOne_1438 → T_IsEquivalence_28 Source #

d_isNearSemiring_1500 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeSemiringWithoutOne_1438 → T_IsNearSemiring_1260 Source #

du_isNearSemiring_1500 ∷ T_IsCommutativeSemiringWithoutOne_1438 → T_IsNearSemiring_1260 Source #

d_isPartialEquivalence_1502 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeSemiringWithoutOne_1438 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_1502 ∷ T_IsCommutativeSemiringWithoutOne_1438 → T_IsPartialEquivalence_16 Source #

d_refl_1504 ∷ T_IsCommutativeSemiringWithoutOne_1438 → AgdaAny → AgdaAny Source #

d_reflexive_1506 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeSemiringWithoutOne_1438 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_1506 ∷ T_IsCommutativeSemiringWithoutOne_1438 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_setoid_1508 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeSemiringWithoutOne_1438 → T_Setoid_46 Source #

du_setoid_1508 ∷ T_IsCommutativeSemiringWithoutOne_1438 → T_Setoid_46 Source #

d_sym_1510 ∷ T_IsCommutativeSemiringWithoutOne_1438 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_1512 ∷ T_IsCommutativeSemiringWithoutOne_1438 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_zero_1514 ∷ T_IsCommutativeSemiringWithoutOne_1438 → T_Σ_14 Source #

d_zero'691'_1516 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeSemiringWithoutOne_1438 → AgdaAny → AgdaAny Source #

du_zero'691'_1516 ∷ T_IsCommutativeSemiringWithoutOne_1438 → AgdaAny → AgdaAny Source #

d_zero'737'_1518 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeSemiringWithoutOne_1438 → AgdaAny → AgdaAny Source #

du_zero'737'_1518 ∷ T_IsCommutativeSemiringWithoutOne_1438 → AgdaAny → AgdaAny Source #

d_'42''45'isCommutativeSemigroup_1520 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeSemiringWithoutOne_1438 → T_IsCommutativeSemigroup_568 Source #

du_'42''45'isCommutativeSemigroup_1520 ∷ T_IsCommutativeSemiringWithoutOne_1438 → T_IsCommutativeSemigroup_568 Source #

d_isCommutativeMagma_1524 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeSemiringWithoutOne_1438 → T_IsCommutativeMagma_214 Source #

du_isCommutativeMagma_1524 ∷ T_IsCommutativeSemiringWithoutOne_1438 → T_IsCommutativeMagma_214 Source #

d_IsSemiringWithoutAnnihilatingZero_1536 ∷ p → p → p → p → p → p → p → p → () Source #

data T_IsSemiringWithoutAnnihilatingZero_1536 Source #

Constructors

C_constructor_1630 T_IsCommutativeMonoid_764 (AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny) (AgdaAny → AgdaAny → AgdaAny → AgdaAny) T_Σ_14 T_Σ_14

d_'43''45'isCommutativeMonoid_1556 ∷ T_IsSemiringWithoutAnnihilatingZero_1536 → T_IsCommutativeMonoid_764 Source #

d_'42''45'cong_1558 ∷ T_IsSemiringWithoutAnnihilatingZero_1536 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'42''45'assoc_1560 ∷ T_IsSemiringWithoutAnnihilatingZero_1536 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'42''45'identity_1562 ∷ T_IsSemiringWithoutAnnihilatingZero_1536 → T_Σ_14 Source #

d_distrib_1564 ∷ T_IsSemiringWithoutAnnihilatingZero_1536 → T_Σ_14 Source #

d_distrib'737'_1566 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiringWithoutAnnihilatingZero_1536 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_distrib'737'_1566 ∷ T_IsSemiringWithoutAnnihilatingZero_1536 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_distrib'691'_1568 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiringWithoutAnnihilatingZero_1536 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_distrib'691'_1568 ∷ T_IsSemiringWithoutAnnihilatingZero_1536 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_assoc_1572 ∷ T_IsSemiringWithoutAnnihilatingZero_1536 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_comm_1574 ∷ T_IsSemiringWithoutAnnihilatingZero_1536 → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_1576 ∷ T_IsSemiringWithoutAnnihilatingZero_1536 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_1578 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiringWithoutAnnihilatingZero_1536 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_1578 ∷ T_IsSemiringWithoutAnnihilatingZero_1536 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_1580 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiringWithoutAnnihilatingZero_1536 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_1580 ∷ T_IsSemiringWithoutAnnihilatingZero_1536 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_identity_1582 ∷ T_IsSemiringWithoutAnnihilatingZero_1536 → T_Σ_14 Source #

d_identity'691'_1584 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiringWithoutAnnihilatingZero_1536 → AgdaAny → AgdaAny Source #

du_identity'691'_1584 ∷ T_IsSemiringWithoutAnnihilatingZero_1536 → AgdaAny → AgdaAny Source #

d_identity'737'_1586 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiringWithoutAnnihilatingZero_1536 → AgdaAny → AgdaAny Source #

du_identity'737'_1586 ∷ T_IsSemiringWithoutAnnihilatingZero_1536 → AgdaAny → AgdaAny Source #

d_isCommutativeMagma_1588 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiringWithoutAnnihilatingZero_1536 → T_IsCommutativeMagma_214 Source #

du_isCommutativeMagma_1588 ∷ T_IsSemiringWithoutAnnihilatingZero_1536 → T_IsCommutativeMagma_214 Source #

d_isCommutativeSemigroup_1590 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiringWithoutAnnihilatingZero_1536 → T_IsCommutativeSemigroup_568 Source #

du_isCommutativeSemigroup_1590 ∷ T_IsSemiringWithoutAnnihilatingZero_1536 → T_IsCommutativeSemigroup_568 Source #

d_isMagma_1592 ∷ T_IsSemiringWithoutAnnihilatingZero_1536 → T_IsMagma_178 Source #

d_isMonoid_1594 ∷ T_IsSemiringWithoutAnnihilatingZero_1536 → T_IsMonoid_712 Source #

d_isSemigroup_1596 ∷ T_IsSemiringWithoutAnnihilatingZero_1536 → T_IsSemigroup_488 Source #

d_isUnitalMagma_1598 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiringWithoutAnnihilatingZero_1536 → T_IsUnitalMagma_666 Source #

du_isUnitalMagma_1598 ∷ T_IsSemiringWithoutAnnihilatingZero_1536 → T_IsUnitalMagma_666 Source #

d_isEquivalence_1600 ∷ T_IsSemiringWithoutAnnihilatingZero_1536 → T_IsEquivalence_28 Source #

d_isPartialEquivalence_1602 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiringWithoutAnnihilatingZero_1536 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_1602 ∷ T_IsSemiringWithoutAnnihilatingZero_1536 → T_IsPartialEquivalence_16 Source #

d_refl_1604 ∷ T_IsSemiringWithoutAnnihilatingZero_1536 → AgdaAny → AgdaAny Source #

d_reflexive_1606 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiringWithoutAnnihilatingZero_1536 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_1606 ∷ T_IsSemiringWithoutAnnihilatingZero_1536 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_setoid_1608 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiringWithoutAnnihilatingZero_1536 → T_Setoid_46 Source #

du_setoid_1608 ∷ T_IsSemiringWithoutAnnihilatingZero_1536 → T_Setoid_46 Source #

d_sym_1610 ∷ T_IsSemiringWithoutAnnihilatingZero_1536 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_1612 ∷ T_IsSemiringWithoutAnnihilatingZero_1536 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'42''45'isMagma_1614 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiringWithoutAnnihilatingZero_1536 → T_IsMagma_178 Source #

du_'42''45'isMagma_1614 ∷ T_IsSemiringWithoutAnnihilatingZero_1536 → T_IsMagma_178 Source #

d_'42''45'isSemigroup_1616 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiringWithoutAnnihilatingZero_1536 → T_IsSemigroup_488 Source #

du_'42''45'isSemigroup_1616 ∷ T_IsSemiringWithoutAnnihilatingZero_1536 → T_IsSemigroup_488 Source #

d_'42''45'isMonoid_1618 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiringWithoutAnnihilatingZero_1536 → T_IsMonoid_712 Source #

du_'42''45'isMonoid_1618 ∷ T_IsSemiringWithoutAnnihilatingZero_1536 → T_IsMonoid_712 Source #

d_'8729''45'cong'691'_1622 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiringWithoutAnnihilatingZero_1536 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_1622 ∷ T_IsSemiringWithoutAnnihilatingZero_1536 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_1624 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiringWithoutAnnihilatingZero_1536 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_1624 ∷ T_IsSemiringWithoutAnnihilatingZero_1536 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_identity'691'_1626 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiringWithoutAnnihilatingZero_1536 → AgdaAny → AgdaAny Source #

du_identity'691'_1626 ∷ T_IsSemiringWithoutAnnihilatingZero_1536 → AgdaAny → AgdaAny Source #

d_identity'737'_1628 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiringWithoutAnnihilatingZero_1536 → AgdaAny → AgdaAny Source #

du_identity'737'_1628 ∷ T_IsSemiringWithoutAnnihilatingZero_1536 → AgdaAny → AgdaAny Source #

d_IsSemiring_1640 ∷ p → p → p → p → p → p → p → p → () Source #

data T_IsSemiring_1640 Source #

Constructors

C_constructor_1740 T_IsSemiringWithoutAnnihilatingZero_1536 T_Σ_14

d_isSemiringWithoutAnnihilatingZero_1654 ∷ T_IsSemiring_1640 → T_IsSemiringWithoutAnnihilatingZero_1536 Source #

d_zero_1656 ∷ T_IsSemiring_1640 → T_Σ_14 Source #

d_'42''45'assoc_1660 ∷ T_IsSemiring_1640 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'42''45'cong_1662 ∷ T_IsSemiring_1640 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_1664 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiring_1640 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_1664 ∷ T_IsSemiring_1640 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_1666 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiring_1640 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_1666 ∷ T_IsSemiring_1640 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'42''45'identity_1668 ∷ T_IsSemiring_1640 → T_Σ_14 Source #

d_identity'691'_1670 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiring_1640 → AgdaAny → AgdaAny Source #

du_identity'691'_1670 ∷ T_IsSemiring_1640 → AgdaAny → AgdaAny Source #

d_identity'737'_1672 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiring_1640 → AgdaAny → AgdaAny Source #

du_identity'737'_1672 ∷ T_IsSemiring_1640 → AgdaAny → AgdaAny Source #

d_'42''45'isMagma_1674 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiring_1640 → T_IsMagma_178 Source #

du_'42''45'isMagma_1674 ∷ T_IsSemiring_1640 → T_IsMagma_178 Source #

d_'42''45'isMonoid_1676 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiring_1640 → T_IsMonoid_712 Source #

du_'42''45'isMonoid_1676 ∷ T_IsSemiring_1640 → T_IsMonoid_712 Source #

d_'42''45'isSemigroup_1678 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiring_1640 → T_IsSemigroup_488 Source #

du_'42''45'isSemigroup_1678 ∷ T_IsSemiring_1640 → T_IsSemigroup_488 Source #

d_assoc_1680 ∷ T_IsSemiring_1640 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_comm_1682 ∷ T_IsSemiring_1640 → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_1684 ∷ T_IsSemiring_1640 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_1686 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiring_1640 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_1686 ∷ T_IsSemiring_1640 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_1688 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiring_1640 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_1688 ∷ T_IsSemiring_1640 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_identity_1690 ∷ T_IsSemiring_1640 → T_Σ_14 Source #

d_identity'691'_1692 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiring_1640 → AgdaAny → AgdaAny Source #

du_identity'691'_1692 ∷ T_IsSemiring_1640 → AgdaAny → AgdaAny Source #

d_identity'737'_1694 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiring_1640 → AgdaAny → AgdaAny Source #

du_identity'737'_1694 ∷ T_IsSemiring_1640 → AgdaAny → AgdaAny Source #

d_isCommutativeMagma_1696 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiring_1640 → T_IsCommutativeMagma_214 Source #

du_isCommutativeMagma_1696 ∷ T_IsSemiring_1640 → T_IsCommutativeMagma_214 Source #

d_'43''45'isCommutativeMonoid_1698 ∷ T_IsSemiring_1640 → T_IsCommutativeMonoid_764 Source #

d_isCommutativeSemigroup_1700 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiring_1640 → T_IsCommutativeSemigroup_568 Source #

du_isCommutativeSemigroup_1700 ∷ T_IsSemiring_1640 → T_IsCommutativeSemigroup_568 Source #

d_isMagma_1702 ∷ T_IsSemiring_1640 → T_IsMagma_178 Source #

d_isMonoid_1704 ∷ T_IsSemiring_1640 → T_IsMonoid_712 Source #

d_isSemigroup_1706 ∷ T_IsSemiring_1640 → T_IsSemigroup_488 Source #

d_isUnitalMagma_1708 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiring_1640 → T_IsUnitalMagma_666 Source #

du_isUnitalMagma_1708 ∷ T_IsSemiring_1640 → T_IsUnitalMagma_666 Source #

d_distrib_1710 ∷ T_IsSemiring_1640 → T_Σ_14 Source #

d_distrib'691'_1712 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiring_1640 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_distrib'691'_1712 ∷ T_IsSemiring_1640 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_distrib'737'_1714 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiring_1640 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_distrib'737'_1714 ∷ T_IsSemiring_1640 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_isEquivalence_1716 ∷ T_IsSemiring_1640 → T_IsEquivalence_28 Source #

d_isPartialEquivalence_1718 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiring_1640 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_1718 ∷ T_IsSemiring_1640 → T_IsPartialEquivalence_16 Source #

d_refl_1720 ∷ T_IsSemiring_1640 → AgdaAny → AgdaAny Source #

d_reflexive_1722 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiring_1640 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_1722 ∷ T_IsSemiring_1640 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_setoid_1724 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiring_1640 → T_Setoid_46 Source #

du_setoid_1724 ∷ T_IsSemiring_1640 → T_Setoid_46 Source #

d_sym_1726 ∷ T_IsSemiring_1640 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_1728 ∷ T_IsSemiring_1640 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_isSemiringWithoutOne_1730 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiring_1640 → T_IsSemiringWithoutOne_1342 Source #

du_isSemiringWithoutOne_1730 ∷ T_IsSemiring_1640 → T_IsSemiringWithoutOne_1342 Source #

d_isNearSemiring_1734 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiring_1640 → T_IsNearSemiring_1260 Source #

du_isNearSemiring_1734 ∷ T_IsSemiring_1640 → T_IsNearSemiring_1260 Source #

d_zero'691'_1736 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiring_1640 → AgdaAny → AgdaAny Source #

du_zero'691'_1736 ∷ T_IsSemiring_1640 → AgdaAny → AgdaAny Source #

d_zero'737'_1738 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiring_1640 → AgdaAny → AgdaAny Source #

du_zero'737'_1738 ∷ T_IsSemiring_1640 → AgdaAny → AgdaAny Source #

d_IsCommutativeSemiring_1750 ∷ p → p → p → p → p → p → p → p → () Source #

data T_IsCommutativeSemiring_1750 Source #

Constructors

C_constructor_1862 T_IsSemiring_1640 (AgdaAny → AgdaAny → AgdaAny)

d_isSemiring_1764 ∷ T_IsCommutativeSemiring_1750 → T_IsSemiring_1640 Source #

d_'42''45'comm_1766 ∷ T_IsCommutativeSemiring_1750 → AgdaAny → AgdaAny → AgdaAny Source #

d_'42''45'assoc_1770 ∷ T_IsCommutativeSemiring_1750 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'42''45'cong_1772 ∷ T_IsCommutativeSemiring_1750 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_1774 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeSemiring_1750 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_1774 ∷ T_IsCommutativeSemiring_1750 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_1776 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeSemiring_1750 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_1776 ∷ T_IsCommutativeSemiring_1750 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'42''45'identity_1778 ∷ T_IsCommutativeSemiring_1750 → T_Σ_14 Source #

d_identity'691'_1780 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeSemiring_1750 → AgdaAny → AgdaAny Source #

du_identity'691'_1780 ∷ T_IsCommutativeSemiring_1750 → AgdaAny → AgdaAny Source #

d_identity'737'_1782 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeSemiring_1750 → AgdaAny → AgdaAny Source #

du_identity'737'_1782 ∷ T_IsCommutativeSemiring_1750 → AgdaAny → AgdaAny Source #

d_'42''45'isMagma_1784 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeSemiring_1750 → T_IsMagma_178 Source #

du_'42''45'isMagma_1784 ∷ T_IsCommutativeSemiring_1750 → T_IsMagma_178 Source #

d_'42''45'isMonoid_1786 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeSemiring_1750 → T_IsMonoid_712 Source #

du_'42''45'isMonoid_1786 ∷ T_IsCommutativeSemiring_1750 → T_IsMonoid_712 Source #

d_'42''45'isSemigroup_1788 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeSemiring_1750 → T_IsSemigroup_488 Source #

du_'42''45'isSemigroup_1788 ∷ T_IsCommutativeSemiring_1750 → T_IsSemigroup_488 Source #

d_assoc_1790 ∷ T_IsCommutativeSemiring_1750 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_comm_1792 ∷ T_IsCommutativeSemiring_1750 → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_1794 ∷ T_IsCommutativeSemiring_1750 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_1796 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeSemiring_1750 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_1796 ∷ T_IsCommutativeSemiring_1750 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_1798 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeSemiring_1750 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_1798 ∷ T_IsCommutativeSemiring_1750 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_identity_1800 ∷ T_IsCommutativeSemiring_1750 → T_Σ_14 Source #

d_identity'691'_1802 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeSemiring_1750 → AgdaAny → AgdaAny Source #

du_identity'691'_1802 ∷ T_IsCommutativeSemiring_1750 → AgdaAny → AgdaAny Source #

d_identity'737'_1804 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeSemiring_1750 → AgdaAny → AgdaAny Source #

du_identity'737'_1804 ∷ T_IsCommutativeSemiring_1750 → AgdaAny → AgdaAny Source #

d_isCommutativeMagma_1806 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeSemiring_1750 → T_IsCommutativeMagma_214 Source #

du_isCommutativeMagma_1806 ∷ T_IsCommutativeSemiring_1750 → T_IsCommutativeMagma_214 Source #

d_'43''45'isCommutativeMonoid_1808 ∷ T_IsCommutativeSemiring_1750 → T_IsCommutativeMonoid_764 Source #

d_isCommutativeSemigroup_1810 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeSemiring_1750 → T_IsCommutativeSemigroup_568 Source #

du_isCommutativeSemigroup_1810 ∷ T_IsCommutativeSemiring_1750 → T_IsCommutativeSemigroup_568 Source #

d_isMagma_1812 ∷ T_IsCommutativeSemiring_1750 → T_IsMagma_178 Source #

d_isMonoid_1814 ∷ T_IsCommutativeSemiring_1750 → T_IsMonoid_712 Source #

d_isSemigroup_1816 ∷ T_IsCommutativeSemiring_1750 → T_IsSemigroup_488 Source #

d_isUnitalMagma_1818 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeSemiring_1750 → T_IsUnitalMagma_666 Source #

du_isUnitalMagma_1818 ∷ T_IsCommutativeSemiring_1750 → T_IsUnitalMagma_666 Source #

d_distrib_1820 ∷ T_IsCommutativeSemiring_1750 → T_Σ_14 Source #

d_distrib'691'_1822 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeSemiring_1750 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_distrib'691'_1822 ∷ T_IsCommutativeSemiring_1750 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_distrib'737'_1824 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeSemiring_1750 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_distrib'737'_1824 ∷ T_IsCommutativeSemiring_1750 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_isEquivalence_1826 ∷ T_IsCommutativeSemiring_1750 → T_IsEquivalence_28 Source #

d_isNearSemiring_1828 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeSemiring_1750 → T_IsNearSemiring_1260 Source #

du_isNearSemiring_1828 ∷ T_IsCommutativeSemiring_1750 → T_IsNearSemiring_1260 Source #

d_isPartialEquivalence_1830 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeSemiring_1750 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_1830 ∷ T_IsCommutativeSemiring_1750 → T_IsPartialEquivalence_16 Source #

d_isSemiringWithoutAnnihilatingZero_1832 ∷ T_IsCommutativeSemiring_1750 → T_IsSemiringWithoutAnnihilatingZero_1536 Source #

d_isSemiringWithoutOne_1834 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeSemiring_1750 → T_IsSemiringWithoutOne_1342 Source #

du_isSemiringWithoutOne_1834 ∷ T_IsCommutativeSemiring_1750 → T_IsSemiringWithoutOne_1342 Source #

d_refl_1836 ∷ T_IsCommutativeSemiring_1750 → AgdaAny → AgdaAny Source #

d_reflexive_1838 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeSemiring_1750 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_1838 ∷ T_IsCommutativeSemiring_1750 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_setoid_1840 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeSemiring_1750 → T_Setoid_46 Source #

du_setoid_1840 ∷ T_IsCommutativeSemiring_1750 → T_Setoid_46 Source #

d_sym_1842 ∷ T_IsCommutativeSemiring_1750 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_1844 ∷ T_IsCommutativeSemiring_1750 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_zero_1846 ∷ T_IsCommutativeSemiring_1750 → T_Σ_14 Source #

d_zero'691'_1848 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeSemiring_1750 → AgdaAny → AgdaAny Source #

du_zero'691'_1848 ∷ T_IsCommutativeSemiring_1750 → AgdaAny → AgdaAny Source #

d_zero'737'_1850 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeSemiring_1750 → AgdaAny → AgdaAny Source #

du_zero'737'_1850 ∷ T_IsCommutativeSemiring_1750 → AgdaAny → AgdaAny Source #

d_isCommutativeSemiringWithoutOne_1852 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeSemiring_1750 → T_IsCommutativeSemiringWithoutOne_1438 Source #

du_isCommutativeSemiringWithoutOne_1852 ∷ T_IsCommutativeSemiring_1750 → T_IsCommutativeSemiringWithoutOne_1438 Source #

d_isCommutativeMagma_1856 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeSemiring_1750 → T_IsCommutativeMagma_214 Source #

du_isCommutativeMagma_1856 ∷ T_IsCommutativeSemiring_1750 → T_IsCommutativeMagma_214 Source #

d_'42''45'isCommutativeSemigroup_1858 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeSemiring_1750 → T_IsCommutativeSemigroup_568 Source #

du_'42''45'isCommutativeSemigroup_1858 ∷ T_IsCommutativeSemiring_1750 → T_IsCommutativeSemigroup_568 Source #

d_'42''45'isCommutativeMonoid_1860 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeSemiring_1750 → T_IsCommutativeMonoid_764 Source #

du_'42''45'isCommutativeMonoid_1860 ∷ T_IsCommutativeSemiring_1750 → T_IsCommutativeMonoid_764 Source #

d_IsCancellativeCommutativeSemiring_1872 ∷ p → p → p → p → p → p → p → p → () Source #

data T_IsCancellativeCommutativeSemiring_1872 Source #

Constructors

C_constructor_1988 T_IsCommutativeSemiring_1750 (AgdaAny → AgdaAny → AgdaAny → (AgdaAny → T_Irrelevant_20) → AgdaAny → AgdaAny)

d_isCommutativeSemiring_1886 ∷ T_IsCancellativeCommutativeSemiring_1872 → T_IsCommutativeSemiring_1750 Source #

d_'42''45'cancel'737''45'nonZero_1888 ∷ T_IsCancellativeCommutativeSemiring_1872 → AgdaAny → AgdaAny → AgdaAny → (AgdaAny → T_Irrelevant_20) → AgdaAny → AgdaAny Source #

d_'42''45'assoc_1892 ∷ T_IsCancellativeCommutativeSemiring_1872 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'42''45'comm_1894 ∷ T_IsCancellativeCommutativeSemiring_1872 → AgdaAny → AgdaAny → AgdaAny Source #

d_'42''45'cong_1896 ∷ T_IsCancellativeCommutativeSemiring_1872 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_1898 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCancellativeCommutativeSemiring_1872 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_1898 ∷ T_IsCancellativeCommutativeSemiring_1872 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_1900 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCancellativeCommutativeSemiring_1872 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_1900 ∷ T_IsCancellativeCommutativeSemiring_1872 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'42''45'identity_1902 ∷ T_IsCancellativeCommutativeSemiring_1872 → T_Σ_14 Source #

d_identity'691'_1904 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCancellativeCommutativeSemiring_1872 → AgdaAny → AgdaAny Source #

du_identity'691'_1904 ∷ T_IsCancellativeCommutativeSemiring_1872 → AgdaAny → AgdaAny Source #

d_identity'737'_1906 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCancellativeCommutativeSemiring_1872 → AgdaAny → AgdaAny Source #

du_identity'737'_1906 ∷ T_IsCancellativeCommutativeSemiring_1872 → AgdaAny → AgdaAny Source #

d_isCommutativeMagma_1908 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCancellativeCommutativeSemiring_1872 → T_IsCommutativeMagma_214 Source #

du_isCommutativeMagma_1908 ∷ T_IsCancellativeCommutativeSemiring_1872 → T_IsCommutativeMagma_214 Source #

d_'42''45'isCommutativeMonoid_1910 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCancellativeCommutativeSemiring_1872 → T_IsCommutativeMonoid_764 Source #

du_'42''45'isCommutativeMonoid_1910 ∷ T_IsCancellativeCommutativeSemiring_1872 → T_IsCommutativeMonoid_764 Source #

d_'42''45'isCommutativeSemigroup_1912 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCancellativeCommutativeSemiring_1872 → T_IsCommutativeSemigroup_568 Source #

du_'42''45'isCommutativeSemigroup_1912 ∷ T_IsCancellativeCommutativeSemiring_1872 → T_IsCommutativeSemigroup_568 Source #

d_'42''45'isMagma_1914 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCancellativeCommutativeSemiring_1872 → T_IsMagma_178 Source #

du_'42''45'isMagma_1914 ∷ T_IsCancellativeCommutativeSemiring_1872 → T_IsMagma_178 Source #

d_'42''45'isMonoid_1916 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCancellativeCommutativeSemiring_1872 → T_IsMonoid_712 Source #

du_'42''45'isMonoid_1916 ∷ T_IsCancellativeCommutativeSemiring_1872 → T_IsMonoid_712 Source #

d_'42''45'isSemigroup_1918 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCancellativeCommutativeSemiring_1872 → T_IsSemigroup_488 Source #

du_'42''45'isSemigroup_1918 ∷ T_IsCancellativeCommutativeSemiring_1872 → T_IsSemigroup_488 Source #

d_assoc_1920 ∷ T_IsCancellativeCommutativeSemiring_1872 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_comm_1922 ∷ T_IsCancellativeCommutativeSemiring_1872 → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_1924 ∷ T_IsCancellativeCommutativeSemiring_1872 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_1926 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCancellativeCommutativeSemiring_1872 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_1926 ∷ T_IsCancellativeCommutativeSemiring_1872 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_1928 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCancellativeCommutativeSemiring_1872 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_1928 ∷ T_IsCancellativeCommutativeSemiring_1872 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_identity_1930 ∷ T_IsCancellativeCommutativeSemiring_1872 → T_Σ_14 Source #

d_identity'691'_1932 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCancellativeCommutativeSemiring_1872 → AgdaAny → AgdaAny Source #

du_identity'691'_1932 ∷ T_IsCancellativeCommutativeSemiring_1872 → AgdaAny → AgdaAny Source #

d_identity'737'_1934 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCancellativeCommutativeSemiring_1872 → AgdaAny → AgdaAny Source #

du_identity'737'_1934 ∷ T_IsCancellativeCommutativeSemiring_1872 → AgdaAny → AgdaAny Source #

d_isCommutativeMagma_1936 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCancellativeCommutativeSemiring_1872 → T_IsCommutativeMagma_214 Source #

du_isCommutativeMagma_1936 ∷ T_IsCancellativeCommutativeSemiring_1872 → T_IsCommutativeMagma_214 Source #

d_'43''45'isCommutativeMonoid_1938 ∷ T_IsCancellativeCommutativeSemiring_1872 → T_IsCommutativeMonoid_764 Source #

d_isCommutativeSemigroup_1940 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCancellativeCommutativeSemiring_1872 → T_IsCommutativeSemigroup_568 Source #

du_isCommutativeSemigroup_1940 ∷ T_IsCancellativeCommutativeSemiring_1872 → T_IsCommutativeSemigroup_568 Source #

d_isMagma_1942 ∷ T_IsCancellativeCommutativeSemiring_1872 → T_IsMagma_178 Source #

d_isMonoid_1944 ∷ T_IsCancellativeCommutativeSemiring_1872 → T_IsMonoid_712 Source #

d_isSemigroup_1946 ∷ T_IsCancellativeCommutativeSemiring_1872 → T_IsSemigroup_488 Source #

d_isUnitalMagma_1948 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCancellativeCommutativeSemiring_1872 → T_IsUnitalMagma_666 Source #

du_isUnitalMagma_1948 ∷ T_IsCancellativeCommutativeSemiring_1872 → T_IsUnitalMagma_666 Source #

d_distrib_1950 ∷ T_IsCancellativeCommutativeSemiring_1872 → T_Σ_14 Source #

d_distrib'691'_1952 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCancellativeCommutativeSemiring_1872 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_distrib'691'_1952 ∷ T_IsCancellativeCommutativeSemiring_1872 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_distrib'737'_1954 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCancellativeCommutativeSemiring_1872 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_distrib'737'_1954 ∷ T_IsCancellativeCommutativeSemiring_1872 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_isCommutativeSemiringWithoutOne_1956 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCancellativeCommutativeSemiring_1872 → T_IsCommutativeSemiringWithoutOne_1438 Source #

du_isCommutativeSemiringWithoutOne_1956 ∷ T_IsCancellativeCommutativeSemiring_1872 → T_IsCommutativeSemiringWithoutOne_1438 Source #

d_isEquivalence_1958 ∷ T_IsCancellativeCommutativeSemiring_1872 → T_IsEquivalence_28 Source #

d_isNearSemiring_1960 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCancellativeCommutativeSemiring_1872 → T_IsNearSemiring_1260 Source #

du_isNearSemiring_1960 ∷ T_IsCancellativeCommutativeSemiring_1872 → T_IsNearSemiring_1260 Source #

d_isPartialEquivalence_1962 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCancellativeCommutativeSemiring_1872 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_1962 ∷ T_IsCancellativeCommutativeSemiring_1872 → T_IsPartialEquivalence_16 Source #

d_isSemiring_1964 ∷ T_IsCancellativeCommutativeSemiring_1872 → T_IsSemiring_1640 Source #

d_isSemiringWithoutAnnihilatingZero_1966 ∷ T_IsCancellativeCommutativeSemiring_1872 → T_IsSemiringWithoutAnnihilatingZero_1536 Source #

d_isSemiringWithoutOne_1968 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCancellativeCommutativeSemiring_1872 → T_IsSemiringWithoutOne_1342 Source #

du_isSemiringWithoutOne_1968 ∷ T_IsCancellativeCommutativeSemiring_1872 → T_IsSemiringWithoutOne_1342 Source #

d_refl_1970 ∷ T_IsCancellativeCommutativeSemiring_1872 → AgdaAny → AgdaAny Source #

d_reflexive_1972 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCancellativeCommutativeSemiring_1872 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_1972 ∷ T_IsCancellativeCommutativeSemiring_1872 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_setoid_1974 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCancellativeCommutativeSemiring_1872 → T_Setoid_46 Source #

du_setoid_1974 ∷ T_IsCancellativeCommutativeSemiring_1872 → T_Setoid_46 Source #

d_sym_1976 ∷ T_IsCancellativeCommutativeSemiring_1872 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_1978 ∷ T_IsCancellativeCommutativeSemiring_1872 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_zero_1980 ∷ T_IsCancellativeCommutativeSemiring_1872 → T_Σ_14 Source #

d_zero'691'_1982 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCancellativeCommutativeSemiring_1872 → AgdaAny → AgdaAny Source #

du_zero'691'_1982 ∷ T_IsCancellativeCommutativeSemiring_1872 → AgdaAny → AgdaAny Source #

d_zero'737'_1984 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCancellativeCommutativeSemiring_1872 → AgdaAny → AgdaAny Source #

du_zero'737'_1984 ∷ T_IsCancellativeCommutativeSemiring_1872 → AgdaAny → AgdaAny Source #

d_'42''45'cancel'691''45'nonZero_1986 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCancellativeCommutativeSemiring_1872 → AgdaAny → AgdaAny → AgdaAny → (AgdaAny → T_Irrelevant_20) → AgdaAny → AgdaAny Source #

du_'42''45'cancel'691''45'nonZero_1986 ∷ (AgdaAny → AgdaAny → AgdaAny) → T_IsCancellativeCommutativeSemiring_1872 → AgdaAny → AgdaAny → AgdaAny → (AgdaAny → T_Irrelevant_20) → AgdaAny → AgdaAny Source #

d_IsIdempotentSemiring_1998 ∷ p → p → p → p → p → p → p → p → () Source #

data T_IsIdempotentSemiring_1998 Source #

Constructors

C_constructor_2110 T_IsSemiring_1640 (AgdaAny → AgdaAny)

d_isSemiring_2012 ∷ T_IsIdempotentSemiring_1998 → T_IsSemiring_1640 Source #

d_'43''45'idem_2014 ∷ T_IsIdempotentSemiring_1998 → AgdaAny → AgdaAny Source #

d_'42''45'assoc_2018 ∷ T_IsIdempotentSemiring_1998 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'42''45'cong_2020 ∷ T_IsIdempotentSemiring_1998 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_2022 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsIdempotentSemiring_1998 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_2022 ∷ T_IsIdempotentSemiring_1998 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_2024 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsIdempotentSemiring_1998 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_2024 ∷ T_IsIdempotentSemiring_1998 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'42''45'identity_2026 ∷ T_IsIdempotentSemiring_1998 → T_Σ_14 Source #

d_identity'691'_2028 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsIdempotentSemiring_1998 → AgdaAny → AgdaAny Source #

du_identity'691'_2028 ∷ T_IsIdempotentSemiring_1998 → AgdaAny → AgdaAny Source #

d_identity'737'_2030 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsIdempotentSemiring_1998 → AgdaAny → AgdaAny Source #

du_identity'737'_2030 ∷ T_IsIdempotentSemiring_1998 → AgdaAny → AgdaAny Source #

d_'42''45'isMagma_2032 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsIdempotentSemiring_1998 → T_IsMagma_178 Source #

du_'42''45'isMagma_2032 ∷ T_IsIdempotentSemiring_1998 → T_IsMagma_178 Source #

d_'42''45'isMonoid_2034 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsIdempotentSemiring_1998 → T_IsMonoid_712 Source #

du_'42''45'isMonoid_2034 ∷ T_IsIdempotentSemiring_1998 → T_IsMonoid_712 Source #

d_'42''45'isSemigroup_2036 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsIdempotentSemiring_1998 → T_IsSemigroup_488 Source #

du_'42''45'isSemigroup_2036 ∷ T_IsIdempotentSemiring_1998 → T_IsSemigroup_488 Source #

d_assoc_2038 ∷ T_IsIdempotentSemiring_1998 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_comm_2040 ∷ T_IsIdempotentSemiring_1998 → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_2042 ∷ T_IsIdempotentSemiring_1998 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_2044 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsIdempotentSemiring_1998 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_2044 ∷ T_IsIdempotentSemiring_1998 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_2046 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsIdempotentSemiring_1998 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_2046 ∷ T_IsIdempotentSemiring_1998 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_identity_2048 ∷ T_IsIdempotentSemiring_1998 → T_Σ_14 Source #

d_identity'691'_2050 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsIdempotentSemiring_1998 → AgdaAny → AgdaAny Source #

du_identity'691'_2050 ∷ T_IsIdempotentSemiring_1998 → AgdaAny → AgdaAny Source #

d_identity'737'_2052 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsIdempotentSemiring_1998 → AgdaAny → AgdaAny Source #

du_identity'737'_2052 ∷ T_IsIdempotentSemiring_1998 → AgdaAny → AgdaAny Source #

d_isCommutativeMagma_2054 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsIdempotentSemiring_1998 → T_IsCommutativeMagma_214 Source #

du_isCommutativeMagma_2054 ∷ T_IsIdempotentSemiring_1998 → T_IsCommutativeMagma_214 Source #

d_'43''45'isCommutativeMonoid_2056 ∷ T_IsIdempotentSemiring_1998 → T_IsCommutativeMonoid_764 Source #

d_isCommutativeSemigroup_2058 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsIdempotentSemiring_1998 → T_IsCommutativeSemigroup_568 Source #

du_isCommutativeSemigroup_2058 ∷ T_IsIdempotentSemiring_1998 → T_IsCommutativeSemigroup_568 Source #

d_isMagma_2060 ∷ T_IsIdempotentSemiring_1998 → T_IsMagma_178 Source #

d_isMonoid_2062 ∷ T_IsIdempotentSemiring_1998 → T_IsMonoid_712 Source #

d_isSemigroup_2064 ∷ T_IsIdempotentSemiring_1998 → T_IsSemigroup_488 Source #

d_isUnitalMagma_2066 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsIdempotentSemiring_1998 → T_IsUnitalMagma_666 Source #

du_isUnitalMagma_2066 ∷ T_IsIdempotentSemiring_1998 → T_IsUnitalMagma_666 Source #

d_distrib_2068 ∷ T_IsIdempotentSemiring_1998 → T_Σ_14 Source #

d_distrib'691'_2070 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsIdempotentSemiring_1998 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_distrib'691'_2070 ∷ T_IsIdempotentSemiring_1998 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_distrib'737'_2072 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsIdempotentSemiring_1998 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_distrib'737'_2072 ∷ T_IsIdempotentSemiring_1998 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_isEquivalence_2074 ∷ T_IsIdempotentSemiring_1998 → T_IsEquivalence_28 Source #

d_isNearSemiring_2076 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsIdempotentSemiring_1998 → T_IsNearSemiring_1260 Source #

du_isNearSemiring_2076 ∷ T_IsIdempotentSemiring_1998 → T_IsNearSemiring_1260 Source #

d_isPartialEquivalence_2078 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsIdempotentSemiring_1998 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_2078 ∷ T_IsIdempotentSemiring_1998 → T_IsPartialEquivalence_16 Source #

d_isSemiringWithoutAnnihilatingZero_2080 ∷ T_IsIdempotentSemiring_1998 → T_IsSemiringWithoutAnnihilatingZero_1536 Source #

d_isSemiringWithoutOne_2082 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsIdempotentSemiring_1998 → T_IsSemiringWithoutOne_1342 Source #

du_isSemiringWithoutOne_2082 ∷ T_IsIdempotentSemiring_1998 → T_IsSemiringWithoutOne_1342 Source #

d_refl_2084 ∷ T_IsIdempotentSemiring_1998 → AgdaAny → AgdaAny Source #

d_reflexive_2086 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsIdempotentSemiring_1998 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_2086 ∷ T_IsIdempotentSemiring_1998 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_setoid_2088 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsIdempotentSemiring_1998 → T_Setoid_46 Source #

du_setoid_2088 ∷ T_IsIdempotentSemiring_1998 → T_Setoid_46 Source #

d_sym_2090 ∷ T_IsIdempotentSemiring_1998 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_2092 ∷ T_IsIdempotentSemiring_1998 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_zero_2094 ∷ T_IsIdempotentSemiring_1998 → T_Σ_14 Source #

d_zero'691'_2096 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsIdempotentSemiring_1998 → AgdaAny → AgdaAny Source #

du_zero'691'_2096 ∷ T_IsIdempotentSemiring_1998 → AgdaAny → AgdaAny Source #

d_zero'737'_2098 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsIdempotentSemiring_1998 → AgdaAny → AgdaAny Source #

du_zero'737'_2098 ∷ T_IsIdempotentSemiring_1998 → AgdaAny → AgdaAny Source #

d_'43''45'isIdempotentCommutativeMonoid_2100 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsIdempotentSemiring_1998 → T_IsIdempotentCommutativeMonoid_884 Source #

du_'43''45'isIdempotentCommutativeMonoid_2100 ∷ T_IsIdempotentSemiring_1998 → T_IsIdempotentCommutativeMonoid_884 Source #

d_isBand_2104 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsIdempotentSemiring_1998 → T_IsBand_526 Source #

du_isBand_2104 ∷ T_IsIdempotentSemiring_1998 → T_IsBand_526 Source #

d_isCommutativeBand_2106 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsIdempotentSemiring_1998 → T_IsCommutativeBand_612 Source #

du_isCommutativeBand_2106 ∷ T_IsIdempotentSemiring_1998 → T_IsCommutativeBand_612 Source #

d_isIdempotentMonoid_2108 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsIdempotentSemiring_1998 → T_IsIdempotentMonoid_826 Source #

du_isIdempotentMonoid_2108 ∷ T_IsIdempotentSemiring_1998 → T_IsIdempotentMonoid_826 Source #

d_IsKleeneAlgebra_2122 ∷ p → p → p → p → p → p → p → p → p → () Source #

data T_IsKleeneAlgebra_2122 Source #

Constructors

C_constructor_2250 T_IsIdempotentSemiring_1998 T_Σ_14 T_Σ_14

d_isIdempotentSemiring_2140 ∷ T_IsKleeneAlgebra_2122 → T_IsIdempotentSemiring_1998 Source #

d_starExpansive_2142 ∷ T_IsKleeneAlgebra_2122 → T_Σ_14 Source #

d_starDestructive_2144 ∷ T_IsKleeneAlgebra_2122 → T_Σ_14 Source #

d_'42''45'assoc_2148 ∷ T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'42''45'cong_2150 ∷ T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_2152 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_2152 ∷ T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_2154 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_2154 ∷ T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'42''45'identity_2156 ∷ T_IsKleeneAlgebra_2122 → T_Σ_14 Source #

d_identity'691'_2158 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny Source #

du_identity'691'_2158 ∷ T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny Source #

d_identity'737'_2160 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny Source #

du_identity'737'_2160 ∷ T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny Source #

d_'42''45'isMagma_2162 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsKleeneAlgebra_2122 → T_IsMagma_178 Source #

du_'42''45'isMagma_2162 ∷ T_IsKleeneAlgebra_2122 → T_IsMagma_178 Source #

d_'42''45'isMonoid_2164 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsKleeneAlgebra_2122 → T_IsMonoid_712 Source #

du_'42''45'isMonoid_2164 ∷ T_IsKleeneAlgebra_2122 → T_IsMonoid_712 Source #

d_'42''45'isSemigroup_2166 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsKleeneAlgebra_2122 → T_IsSemigroup_488 Source #

du_'42''45'isSemigroup_2166 ∷ T_IsKleeneAlgebra_2122 → T_IsSemigroup_488 Source #

d_assoc_2168 ∷ T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_comm_2170 ∷ T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_2172 ∷ T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_2174 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_2174 ∷ T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_2176 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_2176 ∷ T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'43''45'idem_2178 ∷ T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny Source #

d_identity_2180 ∷ T_IsKleeneAlgebra_2122 → T_Σ_14 Source #

d_identity'691'_2182 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny Source #

du_identity'691'_2182 ∷ T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny Source #

d_identity'737'_2184 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny Source #

du_identity'737'_2184 ∷ T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny Source #

d_isBand_2186 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsKleeneAlgebra_2122 → T_IsBand_526 Source #

du_isBand_2186 ∷ T_IsKleeneAlgebra_2122 → T_IsBand_526 Source #

d_isCommutativeBand_2188 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsKleeneAlgebra_2122 → T_IsCommutativeBand_612 Source #

du_isCommutativeBand_2188 ∷ T_IsKleeneAlgebra_2122 → T_IsCommutativeBand_612 Source #

d_isCommutativeMagma_2190 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsKleeneAlgebra_2122 → T_IsCommutativeMagma_214 Source #

du_isCommutativeMagma_2190 ∷ T_IsKleeneAlgebra_2122 → T_IsCommutativeMagma_214 Source #

d_'43''45'isCommutativeMonoid_2192 ∷ T_IsKleeneAlgebra_2122 → T_IsCommutativeMonoid_764 Source #

d_isCommutativeSemigroup_2194 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsKleeneAlgebra_2122 → T_IsCommutativeSemigroup_568 Source #

du_isCommutativeSemigroup_2194 ∷ T_IsKleeneAlgebra_2122 → T_IsCommutativeSemigroup_568 Source #

d_'43''45'isIdempotentCommutativeMonoid_2196 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsKleeneAlgebra_2122 → T_IsIdempotentCommutativeMonoid_884 Source #

du_'43''45'isIdempotentCommutativeMonoid_2196 ∷ T_IsKleeneAlgebra_2122 → T_IsIdempotentCommutativeMonoid_884 Source #

d_isIdempotentMonoid_2198 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsKleeneAlgebra_2122 → T_IsIdempotentMonoid_826 Source #

du_isIdempotentMonoid_2198 ∷ T_IsKleeneAlgebra_2122 → T_IsIdempotentMonoid_826 Source #

d_isMagma_2200 ∷ T_IsKleeneAlgebra_2122 → T_IsMagma_178 Source #

d_isMonoid_2202 ∷ T_IsKleeneAlgebra_2122 → T_IsMonoid_712 Source #

d_isSemigroup_2204 ∷ T_IsKleeneAlgebra_2122 → T_IsSemigroup_488 Source #

d_isUnitalMagma_2206 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsKleeneAlgebra_2122 → T_IsUnitalMagma_666 Source #

du_isUnitalMagma_2206 ∷ T_IsKleeneAlgebra_2122 → T_IsUnitalMagma_666 Source #

d_distrib_2208 ∷ T_IsKleeneAlgebra_2122 → T_Σ_14 Source #

d_distrib'691'_2210 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_distrib'691'_2210 ∷ T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_distrib'737'_2212 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_distrib'737'_2212 ∷ T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_isEquivalence_2214 ∷ T_IsKleeneAlgebra_2122 → T_IsEquivalence_28 Source #

d_isNearSemiring_2216 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsKleeneAlgebra_2122 → T_IsNearSemiring_1260 Source #

du_isNearSemiring_2216 ∷ T_IsKleeneAlgebra_2122 → T_IsNearSemiring_1260 Source #

d_isPartialEquivalence_2218 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsKleeneAlgebra_2122 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_2218 ∷ T_IsKleeneAlgebra_2122 → T_IsPartialEquivalence_16 Source #

d_isSemiring_2220 ∷ T_IsKleeneAlgebra_2122 → T_IsSemiring_1640 Source #

d_isSemiringWithoutAnnihilatingZero_2222 ∷ T_IsKleeneAlgebra_2122 → T_IsSemiringWithoutAnnihilatingZero_1536 Source #

d_isSemiringWithoutOne_2224 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsKleeneAlgebra_2122 → T_IsSemiringWithoutOne_1342 Source #

du_isSemiringWithoutOne_2224 ∷ T_IsKleeneAlgebra_2122 → T_IsSemiringWithoutOne_1342 Source #

d_refl_2226 ∷ T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny Source #

d_reflexive_2228 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_2228 ∷ T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_setoid_2230 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsKleeneAlgebra_2122 → T_Setoid_46 Source #

du_setoid_2230 ∷ T_IsKleeneAlgebra_2122 → T_Setoid_46 Source #

d_sym_2232 ∷ T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_2234 ∷ T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_zero_2236 ∷ T_IsKleeneAlgebra_2122 → T_Σ_14 Source #

d_zero'691'_2238 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny Source #

du_zero'691'_2238 ∷ T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny Source #

d_zero'737'_2240 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny Source #

du_zero'737'_2240 ∷ T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny Source #

d_starExpansive'737'_2242 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny Source #

du_starExpansive'737'_2242 ∷ T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny Source #

d_starExpansive'691'_2244 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny Source #

du_starExpansive'691'_2244 ∷ T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny Source #

d_starDestructive'737'_2246 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_starDestructive'737'_2246 ∷ T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_starDestructive'691'_2248 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_starDestructive'691'_2248 ∷ T_IsKleeneAlgebra_2122 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_IsQuasiring_2260 ∷ p → p → p → p → p → p → p → p → () Source #

data T_IsQuasiring_2260 Source #

Constructors

C_constructor_2358 T_IsMonoid_712 (AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny) (AgdaAny → AgdaAny → AgdaAny → AgdaAny) T_Σ_14 T_Σ_14 T_Σ_14

d_'43''45'isMonoid_2282 ∷ T_IsQuasiring_2260 → T_IsMonoid_712 Source #

d_'42''45'cong_2284 ∷ T_IsQuasiring_2260 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'42''45'assoc_2286 ∷ T_IsQuasiring_2260 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'42''45'identity_2288 ∷ T_IsQuasiring_2260 → T_Σ_14 Source #

d_distrib_2290 ∷ T_IsQuasiring_2260 → T_Σ_14 Source #

d_zero_2292 ∷ T_IsQuasiring_2260 → T_Σ_14 Source #

d_assoc_2296 ∷ T_IsQuasiring_2260 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_2298 ∷ T_IsQuasiring_2260 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_2300 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsQuasiring_2260 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_2300 ∷ T_IsQuasiring_2260 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_2302 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsQuasiring_2260 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_2302 ∷ T_IsQuasiring_2260 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_identity_2304 ∷ T_IsQuasiring_2260 → T_Σ_14 Source #

d_identity'691'_2306 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsQuasiring_2260 → AgdaAny → AgdaAny Source #

du_identity'691'_2306 ∷ T_IsQuasiring_2260 → AgdaAny → AgdaAny Source #

d_identity'737'_2308 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsQuasiring_2260 → AgdaAny → AgdaAny Source #

du_identity'737'_2308 ∷ T_IsQuasiring_2260 → AgdaAny → AgdaAny Source #

d_isMagma_2310 ∷ T_IsQuasiring_2260 → T_IsMagma_178 Source #

d_isSemigroup_2312 ∷ T_IsQuasiring_2260 → T_IsSemigroup_488 Source #

d_isUnitalMagma_2314 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsQuasiring_2260 → T_IsUnitalMagma_666 Source #

du_isUnitalMagma_2314 ∷ T_IsQuasiring_2260 → T_IsUnitalMagma_666 Source #

d_isEquivalence_2316 ∷ T_IsQuasiring_2260 → T_IsEquivalence_28 Source #

d_isPartialEquivalence_2318 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsQuasiring_2260 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_2318 ∷ T_IsQuasiring_2260 → T_IsPartialEquivalence_16 Source #

d_refl_2320 ∷ T_IsQuasiring_2260 → AgdaAny → AgdaAny Source #

d_reflexive_2322 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsQuasiring_2260 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_2322 ∷ T_IsQuasiring_2260 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_setoid_2324 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsQuasiring_2260 → T_Setoid_46 Source #

du_setoid_2324 ∷ T_IsQuasiring_2260 → T_Setoid_46 Source #

d_sym_2326 ∷ T_IsQuasiring_2260 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_2328 ∷ T_IsQuasiring_2260 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_distrib'737'_2330 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsQuasiring_2260 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_distrib'737'_2330 ∷ T_IsQuasiring_2260 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_distrib'691'_2332 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsQuasiring_2260 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_distrib'691'_2332 ∷ T_IsQuasiring_2260 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_zero'737'_2334 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsQuasiring_2260 → AgdaAny → AgdaAny Source #

du_zero'737'_2334 ∷ T_IsQuasiring_2260 → AgdaAny → AgdaAny Source #

d_zero'691'_2336 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsQuasiring_2260 → AgdaAny → AgdaAny Source #

du_zero'691'_2336 ∷ T_IsQuasiring_2260 → AgdaAny → AgdaAny Source #

d_identity'737'_2338 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsQuasiring_2260 → AgdaAny → AgdaAny Source #

du_identity'737'_2338 ∷ T_IsQuasiring_2260 → AgdaAny → AgdaAny Source #

d_identity'691'_2340 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsQuasiring_2260 → AgdaAny → AgdaAny Source #

du_identity'691'_2340 ∷ T_IsQuasiring_2260 → AgdaAny → AgdaAny Source #

d_'42''45'isMagma_2342 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsQuasiring_2260 → T_IsMagma_178 Source #

du_'42''45'isMagma_2342 ∷ T_IsQuasiring_2260 → T_IsMagma_178 Source #

d_'42''45'isSemigroup_2344 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsQuasiring_2260 → T_IsSemigroup_488 Source #

du_'42''45'isSemigroup_2344 ∷ T_IsQuasiring_2260 → T_IsSemigroup_488 Source #

d_'42''45'isMonoid_2346 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsQuasiring_2260 → T_IsMonoid_712 Source #

du_'42''45'isMonoid_2346 ∷ T_IsQuasiring_2260 → T_IsMonoid_712 Source #

d_'8729''45'cong'691'_2350 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsQuasiring_2260 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_2350 ∷ T_IsQuasiring_2260 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_2352 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsQuasiring_2260 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_2352 ∷ T_IsQuasiring_2260 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_identity'691'_2354 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsQuasiring_2260 → AgdaAny → AgdaAny Source #

du_identity'691'_2354 ∷ T_IsQuasiring_2260 → AgdaAny → AgdaAny Source #

d_identity'737'_2356 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsQuasiring_2260 → AgdaAny → AgdaAny Source #

du_identity'737'_2356 ∷ T_IsQuasiring_2260 → AgdaAny → AgdaAny Source #

d_IsRingWithoutOne_2368 ∷ p → p → p → p → p → p → p → p → () Source #

data T_IsRingWithoutOne_2368 Source #

Constructors

C_constructor_2482 T_IsAbelianGroup_1172 (AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny) (AgdaAny → AgdaAny → AgdaAny → AgdaAny) T_Σ_14

d_'43''45'isAbelianGroup_2386 ∷ T_IsRingWithoutOne_2368 → T_IsAbelianGroup_1172 Source #

d_'42''45'cong_2388 ∷ T_IsRingWithoutOne_2368 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'42''45'assoc_2390 ∷ T_IsRingWithoutOne_2368 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_distrib_2392 ∷ T_IsRingWithoutOne_2368 → T_Σ_14 Source #

d__'47''47'__2396 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutOne_2368 → AgdaAny → AgdaAny → AgdaAny Source #

du__'47''47'__2396 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → AgdaAny Source #

d_assoc_2398 ∷ T_IsRingWithoutOne_2368 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_comm_2400 ∷ T_IsRingWithoutOne_2368 → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_2402 ∷ T_IsRingWithoutOne_2368 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_2404 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutOne_2368 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_2404 ∷ T_IsRingWithoutOne_2368 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_2406 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutOne_2368 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_2406 ∷ T_IsRingWithoutOne_2368 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_identity_2408 ∷ T_IsRingWithoutOne_2368 → T_Σ_14 Source #

d_identity'691'_2410 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutOne_2368 → AgdaAny → AgdaAny Source #

du_identity'691'_2410 ∷ T_IsRingWithoutOne_2368 → AgdaAny → AgdaAny Source #

d_identity'737'_2412 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutOne_2368 → AgdaAny → AgdaAny Source #

du_identity'737'_2412 ∷ T_IsRingWithoutOne_2368 → AgdaAny → AgdaAny Source #

d_isCommutativeMagma_2414 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutOne_2368 → T_IsCommutativeMagma_214 Source #

du_isCommutativeMagma_2414 ∷ T_IsRingWithoutOne_2368 → T_IsCommutativeMagma_214 Source #

d_isCommutativeMonoid_2416 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutOne_2368 → T_IsCommutativeMonoid_764 Source #

du_isCommutativeMonoid_2416 ∷ T_IsRingWithoutOne_2368 → T_IsCommutativeMonoid_764 Source #

d_isCommutativeSemigroup_2418 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutOne_2368 → T_IsCommutativeSemigroup_568 Source #

du_isCommutativeSemigroup_2418 ∷ T_IsRingWithoutOne_2368 → T_IsCommutativeSemigroup_568 Source #

d_isGroup_2420 ∷ T_IsRingWithoutOne_2368 → T_IsGroup_1074 Source #

d_isInvertibleMagma_2422 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutOne_2368 → T_IsInvertibleMagma_958 Source #

du_isInvertibleMagma_2422 ∷ T_IsRingWithoutOne_2368 → T_IsInvertibleMagma_958 Source #

d_isInvertibleUnitalMagma_2424 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutOne_2368 → T_IsInvertibleUnitalMagma_1012 Source #

du_isInvertibleUnitalMagma_2424 ∷ T_IsRingWithoutOne_2368 → T_IsInvertibleUnitalMagma_1012 Source #

d_isMagma_2426 ∷ T_IsRingWithoutOne_2368 → T_IsMagma_178 Source #

d_isMonoid_2428 ∷ T_IsRingWithoutOne_2368 → T_IsMonoid_712 Source #

d_isSemigroup_2430 ∷ T_IsRingWithoutOne_2368 → T_IsSemigroup_488 Source #

d_isUnitalMagma_2432 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutOne_2368 → T_IsUnitalMagma_666 Source #

du_isUnitalMagma_2432 ∷ T_IsRingWithoutOne_2368 → T_IsUnitalMagma_666 Source #

d_'8315''185''45'cong_2434 ∷ T_IsRingWithoutOne_2368 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_inverse_2436 ∷ T_IsRingWithoutOne_2368 → T_Σ_14 Source #

d_inverse'691'_2438 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutOne_2368 → AgdaAny → AgdaAny Source #

du_inverse'691'_2438 ∷ T_IsRingWithoutOne_2368 → AgdaAny → AgdaAny Source #

d_inverse'737'_2440 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutOne_2368 → AgdaAny → AgdaAny Source #

du_inverse'737'_2440 ∷ T_IsRingWithoutOne_2368 → AgdaAny → AgdaAny Source #

d_isEquivalence_2442 ∷ T_IsRingWithoutOne_2368 → T_IsEquivalence_28 Source #

d_isPartialEquivalence_2444 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutOne_2368 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_2444 ∷ T_IsRingWithoutOne_2368 → T_IsPartialEquivalence_16 Source #

d_refl_2446 ∷ T_IsRingWithoutOne_2368 → AgdaAny → AgdaAny Source #

d_reflexive_2448 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutOne_2368 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_2448 ∷ T_IsRingWithoutOne_2368 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_setoid_2450 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutOne_2368 → T_Setoid_46 Source #

du_setoid_2450 ∷ T_IsRingWithoutOne_2368 → T_Setoid_46 Source #

d_sym_2452 ∷ T_IsRingWithoutOne_2368 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_2454 ∷ T_IsRingWithoutOne_2368 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_unique'691''45''8315''185'_2456 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutOne_2368 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_unique'691''45''8315''185'_2456 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutOne_2368 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_unique'737''45''8315''185'_2458 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutOne_2368 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_unique'737''45''8315''185'_2458 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutOne_2368 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_distrib'737'_2460 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutOne_2368 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_distrib'737'_2460 ∷ T_IsRingWithoutOne_2368 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_distrib'691'_2462 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutOne_2368 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_distrib'691'_2462 ∷ T_IsRingWithoutOne_2368 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_zero'737'_2464 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutOne_2368 → AgdaAny → AgdaAny Source #

du_zero'737'_2464 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutOne_2368 → AgdaAny → AgdaAny Source #

d_zero'691'_2466 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutOne_2368 → AgdaAny → AgdaAny Source #

du_zero'691'_2466 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutOne_2368 → AgdaAny → AgdaAny Source #

d_zero_2468 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutOne_2368 → T_Σ_14 Source #

du_zero_2468 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutOne_2368 → T_Σ_14 Source #

d_isNearSemiring_2470 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutOne_2368 → T_IsNearSemiring_1260 Source #

du_isNearSemiring_2470 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutOne_2368 → T_IsNearSemiring_1260 Source #

d_'8729''45'cong'691'_2474 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutOne_2368 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_2474 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutOne_2368 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_2476 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutOne_2368 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_2476 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutOne_2368 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'42''45'isMagma_2478 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutOne_2368 → T_IsMagma_178 Source #

du_'42''45'isMagma_2478 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutOne_2368 → T_IsMagma_178 Source #

d_'42''45'isSemigroup_2480 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutOne_2368 → T_IsSemigroup_488 Source #

du_'42''45'isSemigroup_2480 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutOne_2368 → T_IsSemigroup_488 Source #

d_IsNonAssociativeRing_2494 ∷ p → p → p → p → p → p → p → p → p → () Source #

data T_IsNonAssociativeRing_2494 Source #

Constructors

C_constructor_2614 T_IsAbelianGroup_1172 (AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny) T_Σ_14 T_Σ_14 T_Σ_14

d_'43''45'isAbelianGroup_2516 ∷ T_IsNonAssociativeRing_2494 → T_IsAbelianGroup_1172 Source #

d_'42''45'cong_2518 ∷ T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'42''45'identity_2520 ∷ T_IsNonAssociativeRing_2494 → T_Σ_14 Source #

d_distrib_2522 ∷ T_IsNonAssociativeRing_2494 → T_Σ_14 Source #

d_zero_2524 ∷ T_IsNonAssociativeRing_2494 → T_Σ_14 Source #

d__'47''47'__2528 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny → AgdaAny Source #

du__'47''47'__2528 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → AgdaAny Source #

d_assoc_2530 ∷ T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_comm_2532 ∷ T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_2534 ∷ T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_2536 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_2536 ∷ T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_2538 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_2538 ∷ T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_identity_2540 ∷ T_IsNonAssociativeRing_2494 → T_Σ_14 Source #

d_identity'691'_2542 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny Source #

du_identity'691'_2542 ∷ T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny Source #

d_identity'737'_2544 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny Source #

du_identity'737'_2544 ∷ T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny Source #

d_isCommutativeMagma_2546 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsNonAssociativeRing_2494 → T_IsCommutativeMagma_214 Source #

du_isCommutativeMagma_2546 ∷ T_IsNonAssociativeRing_2494 → T_IsCommutativeMagma_214 Source #

d_isCommutativeMonoid_2548 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsNonAssociativeRing_2494 → T_IsCommutativeMonoid_764 Source #

du_isCommutativeMonoid_2548 ∷ T_IsNonAssociativeRing_2494 → T_IsCommutativeMonoid_764 Source #

d_isCommutativeSemigroup_2550 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsNonAssociativeRing_2494 → T_IsCommutativeSemigroup_568 Source #

du_isCommutativeSemigroup_2550 ∷ T_IsNonAssociativeRing_2494 → T_IsCommutativeSemigroup_568 Source #

d_isGroup_2552 ∷ T_IsNonAssociativeRing_2494 → T_IsGroup_1074 Source #

d_isInvertibleMagma_2554 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsNonAssociativeRing_2494 → T_IsInvertibleMagma_958 Source #

du_isInvertibleMagma_2554 ∷ T_IsNonAssociativeRing_2494 → T_IsInvertibleMagma_958 Source #

d_isInvertibleUnitalMagma_2556 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsNonAssociativeRing_2494 → T_IsInvertibleUnitalMagma_1012 Source #

du_isInvertibleUnitalMagma_2556 ∷ T_IsNonAssociativeRing_2494 → T_IsInvertibleUnitalMagma_1012 Source #

d_isMagma_2558 ∷ T_IsNonAssociativeRing_2494 → T_IsMagma_178 Source #

d_isMonoid_2560 ∷ T_IsNonAssociativeRing_2494 → T_IsMonoid_712 Source #

d_isSemigroup_2562 ∷ T_IsNonAssociativeRing_2494 → T_IsSemigroup_488 Source #

d_isUnitalMagma_2564 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsNonAssociativeRing_2494 → T_IsUnitalMagma_666 Source #

du_isUnitalMagma_2564 ∷ T_IsNonAssociativeRing_2494 → T_IsUnitalMagma_666 Source #

d_'8315''185''45'cong_2566 ∷ T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_inverse_2568 ∷ T_IsNonAssociativeRing_2494 → T_Σ_14 Source #

d_inverse'691'_2570 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny Source #

du_inverse'691'_2570 ∷ T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny Source #

d_inverse'737'_2572 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny Source #

du_inverse'737'_2572 ∷ T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny Source #

d_isEquivalence_2574 ∷ T_IsNonAssociativeRing_2494 → T_IsEquivalence_28 Source #

d_isPartialEquivalence_2576 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsNonAssociativeRing_2494 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_2576 ∷ T_IsNonAssociativeRing_2494 → T_IsPartialEquivalence_16 Source #

d_refl_2578 ∷ T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny Source #

d_reflexive_2580 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_2580 ∷ T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_setoid_2582 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsNonAssociativeRing_2494 → T_Setoid_46 Source #

du_setoid_2582 ∷ T_IsNonAssociativeRing_2494 → T_Setoid_46 Source #

d_sym_2584 ∷ T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_2586 ∷ T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_unique'691''45''8315''185'_2588 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_unique'691''45''8315''185'_2588 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_unique'737''45''8315''185'_2590 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_unique'737''45''8315''185'_2590 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_zero'737'_2592 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny Source #

du_zero'737'_2592 ∷ T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny Source #

d_zero'691'_2594 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny Source #

du_zero'691'_2594 ∷ T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny Source #

d_distrib'737'_2596 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_distrib'737'_2596 ∷ T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_distrib'691'_2598 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_distrib'691'_2598 ∷ T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'42''45'isMagma_2600 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsNonAssociativeRing_2494 → T_IsMagma_178 Source #

du_'42''45'isMagma_2600 ∷ T_IsNonAssociativeRing_2494 → T_IsMagma_178 Source #

d_'42''45'identity'737'_2602 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny Source #

du_'42''45'identity'737'_2602 ∷ T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny Source #

d_'42''45'identity'691'_2604 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny Source #

du_'42''45'identity'691'_2604 ∷ T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny Source #

d_'42''45'isUnitalMagma_2606 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsNonAssociativeRing_2494 → T_IsUnitalMagma_666 Source #

du_'42''45'isUnitalMagma_2606 ∷ T_IsNonAssociativeRing_2494 → T_IsUnitalMagma_666 Source #

d_'8729''45'cong'691'_2610 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_2610 ∷ T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_2612 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_2612 ∷ T_IsNonAssociativeRing_2494 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_IsNearring_2626 ∷ p → p → p → p → p → p → p → p → p → () Source #

data T_IsNearring_2626 Source #

Constructors

C_constructor_2728 T_IsQuasiring_2260 T_Σ_14 (AgdaAny → AgdaAny → AgdaAny → AgdaAny)

d_isQuasiring_2644 ∷ T_IsNearring_2626 → T_IsQuasiring_2260 Source #

d_'43''45'inverse_2646 ∷ T_IsNearring_2626 → T_Σ_14 Source #

d_'8315''185''45'cong_2648 ∷ T_IsNearring_2626 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'42''45'assoc_2652 ∷ T_IsNearring_2626 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'42''45'cong_2654 ∷ T_IsNearring_2626 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_2656 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → (AgdaAny → AgdaAny) → T_IsNearring_2626 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_2656 ∷ T_IsNearring_2626 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_2658 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → (AgdaAny → AgdaAny) → T_IsNearring_2626 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_2658 ∷ T_IsNearring_2626 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'42''45'identity_2660 ∷ T_IsNearring_2626 → T_Σ_14 Source #

d_identity'691'_2662 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → (AgdaAny → AgdaAny) → T_IsNearring_2626 → AgdaAny → AgdaAny Source #

du_identity'691'_2662 ∷ T_IsNearring_2626 → AgdaAny → AgdaAny Source #

d_identity'737'_2664 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → (AgdaAny → AgdaAny) → T_IsNearring_2626 → AgdaAny → AgdaAny Source #

du_identity'737'_2664 ∷ T_IsNearring_2626 → AgdaAny → AgdaAny Source #

d_'42''45'isMagma_2666 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → (AgdaAny → AgdaAny) → T_IsNearring_2626 → T_IsMagma_178 Source #

du_'42''45'isMagma_2666 ∷ T_IsNearring_2626 → T_IsMagma_178 Source #

d_'42''45'isMonoid_2668 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → (AgdaAny → AgdaAny) → T_IsNearring_2626 → T_IsMonoid_712 Source #

du_'42''45'isMonoid_2668 ∷ T_IsNearring_2626 → T_IsMonoid_712 Source #

d_'42''45'isSemigroup_2670 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → (AgdaAny → AgdaAny) → T_IsNearring_2626 → T_IsSemigroup_488 Source #

du_'42''45'isSemigroup_2670 ∷ T_IsNearring_2626 → T_IsSemigroup_488 Source #

d_assoc_2672 ∷ T_IsNearring_2626 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_2674 ∷ T_IsNearring_2626 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_2676 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → (AgdaAny → AgdaAny) → T_IsNearring_2626 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_2676 ∷ T_IsNearring_2626 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_2678 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → (AgdaAny → AgdaAny) → T_IsNearring_2626 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_2678 ∷ T_IsNearring_2626 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_identity_2680 ∷ T_IsNearring_2626 → T_Σ_14 Source #

d_identity'691'_2682 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → (AgdaAny → AgdaAny) → T_IsNearring_2626 → AgdaAny → AgdaAny Source #

du_identity'691'_2682 ∷ T_IsNearring_2626 → AgdaAny → AgdaAny Source #

d_identity'737'_2684 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → (AgdaAny → AgdaAny) → T_IsNearring_2626 → AgdaAny → AgdaAny Source #

du_identity'737'_2684 ∷ T_IsNearring_2626 → AgdaAny → AgdaAny Source #

d_isMagma_2686 ∷ T_IsNearring_2626 → T_IsMagma_178 Source #

d_'43''45'isMonoid_2688 ∷ T_IsNearring_2626 → T_IsMonoid_712 Source #

d_isSemigroup_2690 ∷ T_IsNearring_2626 → T_IsSemigroup_488 Source #

d_isUnitalMagma_2692 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → (AgdaAny → AgdaAny) → T_IsNearring_2626 → T_IsUnitalMagma_666 Source #

du_isUnitalMagma_2692 ∷ T_IsNearring_2626 → T_IsUnitalMagma_666 Source #

d_distrib_2694 ∷ T_IsNearring_2626 → T_Σ_14 Source #

d_distrib'691'_2696 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → (AgdaAny → AgdaAny) → T_IsNearring_2626 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_distrib'691'_2696 ∷ T_IsNearring_2626 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_distrib'737'_2698 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → (AgdaAny → AgdaAny) → T_IsNearring_2626 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_distrib'737'_2698 ∷ T_IsNearring_2626 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_identity'691'_2700 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → (AgdaAny → AgdaAny) → T_IsNearring_2626 → AgdaAny → AgdaAny Source #

du_identity'691'_2700 ∷ T_IsNearring_2626 → AgdaAny → AgdaAny Source #

d_identity'737'_2702 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → (AgdaAny → AgdaAny) → T_IsNearring_2626 → AgdaAny → AgdaAny Source #

du_identity'737'_2702 ∷ T_IsNearring_2626 → AgdaAny → AgdaAny Source #

d_isEquivalence_2704 ∷ T_IsNearring_2626 → T_IsEquivalence_28 Source #

d_isPartialEquivalence_2706 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → (AgdaAny → AgdaAny) → T_IsNearring_2626 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_2706 ∷ T_IsNearring_2626 → T_IsPartialEquivalence_16 Source #

d_refl_2708 ∷ T_IsNearring_2626 → AgdaAny → AgdaAny Source #

d_reflexive_2710 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → (AgdaAny → AgdaAny) → T_IsNearring_2626 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_2710 ∷ T_IsNearring_2626 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_setoid_2712 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → (AgdaAny → AgdaAny) → T_IsNearring_2626 → T_Setoid_46 Source #

du_setoid_2712 ∷ T_IsNearring_2626 → T_Setoid_46 Source #

d_sym_2714 ∷ T_IsNearring_2626 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_2716 ∷ T_IsNearring_2626 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_zero_2718 ∷ T_IsNearring_2626 → T_Σ_14 Source #

d_zero'691'_2720 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → (AgdaAny → AgdaAny) → T_IsNearring_2626 → AgdaAny → AgdaAny Source #

du_zero'691'_2720 ∷ T_IsNearring_2626 → AgdaAny → AgdaAny Source #

d_zero'737'_2722 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → (AgdaAny → AgdaAny) → T_IsNearring_2626 → AgdaAny → AgdaAny Source #

du_zero'737'_2722 ∷ T_IsNearring_2626 → AgdaAny → AgdaAny Source #

d_'43''45'inverse'737'_2724 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → (AgdaAny → AgdaAny) → T_IsNearring_2626 → AgdaAny → AgdaAny Source #

du_'43''45'inverse'737'_2724 ∷ T_IsNearring_2626 → AgdaAny → AgdaAny Source #

d_'43''45'inverse'691'_2726 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → (AgdaAny → AgdaAny) → T_IsNearring_2626 → AgdaAny → AgdaAny Source #

du_'43''45'inverse'691'_2726 ∷ T_IsNearring_2626 → AgdaAny → AgdaAny Source #

d_IsRing_2740 ∷ p → p → p → p → p → p → p → p → p → () Source #

data T_IsRing_2740 Source #

Constructors

C_constructor_2876 T_IsAbelianGroup_1172 (AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny) (AgdaAny → AgdaAny → AgdaAny → AgdaAny) T_Σ_14 T_Σ_14

d_'43''45'isAbelianGroup_2762 ∷ T_IsRing_2740 → T_IsAbelianGroup_1172 Source #

d_'42''45'cong_2764 ∷ T_IsRing_2740 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'42''45'assoc_2766 ∷ T_IsRing_2740 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'42''45'identity_2768 ∷ T_IsRing_2740 → T_Σ_14 Source #

d_distrib_2770 ∷ T_IsRing_2740 → T_Σ_14 Source #

d_isRingWithoutOne_2772 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → T_IsRingWithoutOne_2368 Source #

du_isRingWithoutOne_2772 ∷ T_IsRing_2740 → T_IsRingWithoutOne_2368 Source #

d__'47''47'__2776 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → AgdaAny → AgdaAny → AgdaAny Source #

du__'47''47'__2776 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_2778 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_2778 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRing_2740 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_2780 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_2780 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRing_2740 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'42''45'isMagma_2782 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → T_IsMagma_178 Source #

du_'42''45'isMagma_2782 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRing_2740 → T_IsMagma_178 Source #

d_'42''45'isSemigroup_2784 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → T_IsSemigroup_488 Source #

du_'42''45'isSemigroup_2784 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRing_2740 → T_IsSemigroup_488 Source #

d_assoc_2786 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_assoc_2786 ∷ T_IsRing_2740 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_comm_2788 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → AgdaAny → AgdaAny → AgdaAny Source #

du_comm_2788 ∷ T_IsRing_2740 → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_2790 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong_2790 ∷ T_IsRing_2740 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_2792 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_2792 ∷ T_IsRing_2740 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_2794 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_2794 ∷ T_IsRing_2740 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_identity_2796 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → T_Σ_14 Source #

du_identity_2796 ∷ T_IsRing_2740 → T_Σ_14 Source #

d_identity'691'_2798 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → AgdaAny → AgdaAny Source #

du_identity'691'_2798 ∷ T_IsRing_2740 → AgdaAny → AgdaAny Source #

d_identity'737'_2800 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → AgdaAny → AgdaAny Source #

du_identity'737'_2800 ∷ T_IsRing_2740 → AgdaAny → AgdaAny Source #

d_isCommutativeMagma_2802 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → T_IsCommutativeMagma_214 Source #

du_isCommutativeMagma_2802 ∷ T_IsRing_2740 → T_IsCommutativeMagma_214 Source #

d_isCommutativeMonoid_2804 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → T_IsCommutativeMonoid_764 Source #

du_isCommutativeMonoid_2804 ∷ T_IsRing_2740 → T_IsCommutativeMonoid_764 Source #

d_isCommutativeSemigroup_2806 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → T_IsCommutativeSemigroup_568 Source #

du_isCommutativeSemigroup_2806 ∷ T_IsRing_2740 → T_IsCommutativeSemigroup_568 Source #

d_isGroup_2808 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → T_IsGroup_1074 Source #

du_isGroup_2808 ∷ T_IsRing_2740 → T_IsGroup_1074 Source #

d_isInvertibleMagma_2810 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → T_IsInvertibleMagma_958 Source #

du_isInvertibleMagma_2810 ∷ T_IsRing_2740 → T_IsInvertibleMagma_958 Source #

d_isInvertibleUnitalMagma_2812 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → T_IsInvertibleUnitalMagma_1012 Source #

du_isInvertibleUnitalMagma_2812 ∷ T_IsRing_2740 → T_IsInvertibleUnitalMagma_1012 Source #

d_isMagma_2814 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → T_IsMagma_178 Source #

du_isMagma_2814 ∷ T_IsRing_2740 → T_IsMagma_178 Source #

d_isMonoid_2816 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → T_IsMonoid_712 Source #

du_isMonoid_2816 ∷ T_IsRing_2740 → T_IsMonoid_712 Source #

d_isSemigroup_2818 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → T_IsSemigroup_488 Source #

du_isSemigroup_2818 ∷ T_IsRing_2740 → T_IsSemigroup_488 Source #

d_isUnitalMagma_2820 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → T_IsUnitalMagma_666 Source #

du_isUnitalMagma_2820 ∷ T_IsRing_2740 → T_IsUnitalMagma_666 Source #

d_'8315''185''45'cong_2822 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8315''185''45'cong_2822 ∷ T_IsRing_2740 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_inverse_2824 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → T_Σ_14 Source #

du_inverse_2824 ∷ T_IsRing_2740 → T_Σ_14 Source #

d_inverse'691'_2826 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → AgdaAny → AgdaAny Source #

du_inverse'691'_2826 ∷ T_IsRing_2740 → AgdaAny → AgdaAny Source #

d_inverse'737'_2828 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → AgdaAny → AgdaAny Source #

du_inverse'737'_2828 ∷ T_IsRing_2740 → AgdaAny → AgdaAny Source #

d_distrib'691'_2830 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_distrib'691'_2830 ∷ T_IsRing_2740 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_distrib'737'_2832 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_distrib'737'_2832 ∷ T_IsRing_2740 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_isEquivalence_2834 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → T_IsEquivalence_28 Source #

du_isEquivalence_2834 ∷ T_IsRing_2740 → T_IsEquivalence_28 Source #

d_isNearSemiring_2836 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → T_IsNearSemiring_1260 Source #

du_isNearSemiring_2836 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRing_2740 → T_IsNearSemiring_1260 Source #

d_isPartialEquivalence_2838 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_2838 ∷ T_IsRing_2740 → T_IsPartialEquivalence_16 Source #

d_refl_2840 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → AgdaAny → AgdaAny Source #

du_refl_2840 ∷ T_IsRing_2740 → AgdaAny → AgdaAny Source #

d_reflexive_2842 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_2842 ∷ T_IsRing_2740 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_setoid_2844 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → T_Setoid_46 Source #

du_setoid_2844 ∷ T_IsRing_2740 → T_Setoid_46 Source #

d_sym_2846 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_sym_2846 ∷ T_IsRing_2740 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_2848 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_trans_2848 ∷ T_IsRing_2740 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_unique'691''45''8315''185'_2850 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_unique'691''45''8315''185'_2850 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRing_2740 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_unique'737''45''8315''185'_2852 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_unique'737''45''8315''185'_2852 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRing_2740 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_zero_2854 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → T_Σ_14 Source #

du_zero_2854 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRing_2740 → T_Σ_14 Source #

d_zero'691'_2856 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → AgdaAny → AgdaAny Source #

du_zero'691'_2856 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRing_2740 → AgdaAny → AgdaAny Source #

d_zero'737'_2858 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → AgdaAny → AgdaAny Source #

du_zero'737'_2858 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRing_2740 → AgdaAny → AgdaAny Source #

d_'42''45'isMonoid_2860 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → T_IsMonoid_712 Source #

du_'42''45'isMonoid_2860 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRing_2740 → T_IsMonoid_712 Source #

d_identity'691'_2864 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → AgdaAny → AgdaAny Source #

du_identity'691'_2864 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRing_2740 → AgdaAny → AgdaAny Source #

d_identity'737'_2866 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → AgdaAny → AgdaAny Source #

du_identity'737'_2866 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRing_2740 → AgdaAny → AgdaAny Source #

d_isSemiringWithoutAnnihilatingZero_2868 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → T_IsSemiringWithoutAnnihilatingZero_1536 Source #

du_isSemiringWithoutAnnihilatingZero_2868 ∷ T_IsRing_2740 → T_IsSemiringWithoutAnnihilatingZero_1536 Source #

d_isSemiring_2870 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → T_IsSemiring_1640 Source #

du_isSemiring_2870 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRing_2740 → T_IsSemiring_1640 Source #

d_isSemiringWithoutOne_2874 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing_2740 → T_IsSemiringWithoutOne_1342 Source #

du_isSemiringWithoutOne_2874 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRing_2740 → T_IsSemiringWithoutOne_1342 Source #

d_IsCommutativeRing_2888 ∷ p → p → p → p → p → p → p → p → p → () Source #

data T_IsCommutativeRing_2888 Source #

Constructors

C_constructor_3030 T_IsRing_2740 (AgdaAny → AgdaAny → AgdaAny)

d_isRing_2904 ∷ T_IsCommutativeRing_2888 → T_IsRing_2740 Source #

d_'42''45'comm_2906 ∷ T_IsCommutativeRing_2888 → AgdaAny → AgdaAny → AgdaAny Source #

d__'47''47'__2910 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → AgdaAny → AgdaAny → AgdaAny Source #

du__'47''47'__2910 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → AgdaAny Source #

d_'42''45'assoc_2912 ∷ T_IsCommutativeRing_2888 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'42''45'cong_2914 ∷ T_IsCommutativeRing_2888 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_2916 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_2916 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeRing_2888 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_2918 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_2918 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeRing_2888 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'42''45'identity_2920 ∷ T_IsCommutativeRing_2888 → T_Σ_14 Source #

d_identity'691'_2922 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → AgdaAny → AgdaAny Source #

du_identity'691'_2922 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeRing_2888 → AgdaAny → AgdaAny Source #

d_identity'737'_2924 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → AgdaAny → AgdaAny Source #

du_identity'737'_2924 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeRing_2888 → AgdaAny → AgdaAny Source #

d_'42''45'isMagma_2926 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → T_IsMagma_178 Source #

du_'42''45'isMagma_2926 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeRing_2888 → T_IsMagma_178 Source #

d_'42''45'isMonoid_2928 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → T_IsMonoid_712 Source #

du_'42''45'isMonoid_2928 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeRing_2888 → T_IsMonoid_712 Source #

d_'42''45'isSemigroup_2930 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → T_IsSemigroup_488 Source #

du_'42''45'isSemigroup_2930 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeRing_2888 → T_IsSemigroup_488 Source #

d_assoc_2932 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_assoc_2932 ∷ T_IsCommutativeRing_2888 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_comm_2934 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → AgdaAny → AgdaAny → AgdaAny Source #

du_comm_2934 ∷ T_IsCommutativeRing_2888 → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_2936 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong_2936 ∷ T_IsCommutativeRing_2888 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_2938 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_2938 ∷ T_IsCommutativeRing_2888 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_2940 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_2940 ∷ T_IsCommutativeRing_2888 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_identity_2942 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → T_Σ_14 Source #

du_identity_2942 ∷ T_IsCommutativeRing_2888 → T_Σ_14 Source #

d_identity'691'_2944 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → AgdaAny → AgdaAny Source #

du_identity'691'_2944 ∷ T_IsCommutativeRing_2888 → AgdaAny → AgdaAny Source #

d_identity'737'_2946 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → AgdaAny → AgdaAny Source #

du_identity'737'_2946 ∷ T_IsCommutativeRing_2888 → AgdaAny → AgdaAny Source #

d_'43''45'isAbelianGroup_2948 ∷ T_IsCommutativeRing_2888 → T_IsAbelianGroup_1172 Source #

d_isCommutativeMagma_2950 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → T_IsCommutativeMagma_214 Source #

du_isCommutativeMagma_2950 ∷ T_IsCommutativeRing_2888 → T_IsCommutativeMagma_214 Source #

d_isCommutativeMonoid_2952 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → T_IsCommutativeMonoid_764 Source #

du_isCommutativeMonoid_2952 ∷ T_IsCommutativeRing_2888 → T_IsCommutativeMonoid_764 Source #

d_isCommutativeSemigroup_2954 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → T_IsCommutativeSemigroup_568 Source #

du_isCommutativeSemigroup_2954 ∷ T_IsCommutativeRing_2888 → T_IsCommutativeSemigroup_568 Source #

d_isGroup_2956 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → T_IsGroup_1074 Source #

du_isGroup_2956 ∷ T_IsCommutativeRing_2888 → T_IsGroup_1074 Source #

d_isInvertibleMagma_2958 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → T_IsInvertibleMagma_958 Source #

du_isInvertibleMagma_2958 ∷ T_IsCommutativeRing_2888 → T_IsInvertibleMagma_958 Source #

d_isInvertibleUnitalMagma_2960 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → T_IsInvertibleUnitalMagma_1012 Source #

du_isInvertibleUnitalMagma_2960 ∷ T_IsCommutativeRing_2888 → T_IsInvertibleUnitalMagma_1012 Source #

d_isMagma_2962 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → T_IsMagma_178 Source #

du_isMagma_2962 ∷ T_IsCommutativeRing_2888 → T_IsMagma_178 Source #

d_isMonoid_2964 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → T_IsMonoid_712 Source #

du_isMonoid_2964 ∷ T_IsCommutativeRing_2888 → T_IsMonoid_712 Source #

d_isSemigroup_2966 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → T_IsSemigroup_488 Source #

du_isSemigroup_2966 ∷ T_IsCommutativeRing_2888 → T_IsSemigroup_488 Source #

d_isUnitalMagma_2968 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → T_IsUnitalMagma_666 Source #

du_isUnitalMagma_2968 ∷ T_IsCommutativeRing_2888 → T_IsUnitalMagma_666 Source #

d_'8315''185''45'cong_2970 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8315''185''45'cong_2970 ∷ T_IsCommutativeRing_2888 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_inverse_2972 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → T_Σ_14 Source #

du_inverse_2972 ∷ T_IsCommutativeRing_2888 → T_Σ_14 Source #

d_inverse'691'_2974 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → AgdaAny → AgdaAny Source #

du_inverse'691'_2974 ∷ T_IsCommutativeRing_2888 → AgdaAny → AgdaAny Source #

d_inverse'737'_2976 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → AgdaAny → AgdaAny Source #

du_inverse'737'_2976 ∷ T_IsCommutativeRing_2888 → AgdaAny → AgdaAny Source #

d_distrib_2978 ∷ T_IsCommutativeRing_2888 → T_Σ_14 Source #

d_distrib'691'_2980 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_distrib'691'_2980 ∷ T_IsCommutativeRing_2888 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_distrib'737'_2982 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_distrib'737'_2982 ∷ T_IsCommutativeRing_2888 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_isEquivalence_2984 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → T_IsEquivalence_28 Source #

du_isEquivalence_2984 ∷ T_IsCommutativeRing_2888 → T_IsEquivalence_28 Source #

d_isNearSemiring_2986 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → T_IsNearSemiring_1260 Source #

du_isNearSemiring_2986 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeRing_2888 → T_IsNearSemiring_1260 Source #

d_isPartialEquivalence_2988 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_2988 ∷ T_IsCommutativeRing_2888 → T_IsPartialEquivalence_16 Source #

d_isRingWithoutOne_2990 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → T_IsRingWithoutOne_2368 Source #

du_isRingWithoutOne_2990 ∷ T_IsCommutativeRing_2888 → T_IsRingWithoutOne_2368 Source #

d_isSemiring_2992 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → T_IsSemiring_1640 Source #

du_isSemiring_2992 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeRing_2888 → T_IsSemiring_1640 Source #

d_isSemiringWithoutAnnihilatingZero_2994 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → T_IsSemiringWithoutAnnihilatingZero_1536 Source #

du_isSemiringWithoutAnnihilatingZero_2994 ∷ T_IsCommutativeRing_2888 → T_IsSemiringWithoutAnnihilatingZero_1536 Source #

d_isSemiringWithoutOne_2996 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → T_IsSemiringWithoutOne_1342 Source #

du_isSemiringWithoutOne_2996 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeRing_2888 → T_IsSemiringWithoutOne_1342 Source #

d_refl_2998 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → AgdaAny → AgdaAny Source #

du_refl_2998 ∷ T_IsCommutativeRing_2888 → AgdaAny → AgdaAny Source #

d_reflexive_3000 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_3000 ∷ T_IsCommutativeRing_2888 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_setoid_3002 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → T_Setoid_46 Source #

du_setoid_3002 ∷ T_IsCommutativeRing_2888 → T_Setoid_46 Source #

d_sym_3004 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_sym_3004 ∷ T_IsCommutativeRing_2888 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_3006 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_trans_3006 ∷ T_IsCommutativeRing_2888 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_unique'691''45''8315''185'_3008 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_unique'691''45''8315''185'_3008 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeRing_2888 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_unique'737''45''8315''185'_3010 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_unique'737''45''8315''185'_3010 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeRing_2888 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_zero_3012 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → T_Σ_14 Source #

du_zero_3012 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeRing_2888 → T_Σ_14 Source #

d_zero'691'_3014 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → AgdaAny → AgdaAny Source #

du_zero'691'_3014 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeRing_2888 → AgdaAny → AgdaAny Source #

d_zero'737'_3016 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → AgdaAny → AgdaAny Source #

du_zero'737'_3016 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeRing_2888 → AgdaAny → AgdaAny Source #

d_isCommutativeSemiring_3018 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → T_IsCommutativeSemiring_1750 Source #

du_isCommutativeSemiring_3018 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeRing_2888 → T_IsCommutativeSemiring_1750 Source #

d_isCommutativeMagma_3022 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → T_IsCommutativeMagma_214 Source #

du_isCommutativeMagma_3022 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeRing_2888 → T_IsCommutativeMagma_214 Source #

d_'42''45'isCommutativeMonoid_3024 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → T_IsCommutativeMonoid_764 Source #

du_'42''45'isCommutativeMonoid_3024 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeRing_2888 → T_IsCommutativeMonoid_764 Source #

d_'42''45'isCommutativeSemigroup_3026 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → T_IsCommutativeSemigroup_568 Source #

du_'42''45'isCommutativeSemigroup_3026 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeRing_2888 → T_IsCommutativeSemigroup_568 Source #

d_isCommutativeSemiringWithoutOne_3028 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeRing_2888 → T_IsCommutativeSemiringWithoutOne_1438 Source #

du_isCommutativeSemiringWithoutOne_3028 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeRing_2888 → T_IsCommutativeSemiringWithoutOne_1438 Source #

d_IsQuasigroup_3038 ∷ p → p → p → p → p → p → p → () Source #

data T_IsQuasigroup_3038 Source #

Constructors

C_constructor_3112 T_IsMagma_178 (AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny) (AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny) T_Σ_14 T_Σ_14

d_isMagma_3056 ∷ T_IsQuasigroup_3038 → T_IsMagma_178 Source #

d_'92''92''45'cong_3058 ∷ T_IsQuasigroup_3038 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'47''47''45'cong_3060 ∷ T_IsQuasigroup_3038 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_leftDivides_3062 ∷ T_IsQuasigroup_3038 → T_Σ_14 Source #

d_rightDivides_3064 ∷ T_IsQuasigroup_3038 → T_Σ_14 Source #

d_isEquivalence_3068 ∷ T_IsQuasigroup_3038 → T_IsEquivalence_28 Source #

d_isPartialEquivalence_3070 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → T_IsQuasigroup_3038 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_3070 ∷ T_IsQuasigroup_3038 → T_IsPartialEquivalence_16 Source #

d_refl_3072 ∷ T_IsQuasigroup_3038 → AgdaAny → AgdaAny Source #

d_reflexive_3074 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → T_IsQuasigroup_3038 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_3074 ∷ T_IsQuasigroup_3038 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_setoid_3076 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → T_IsQuasigroup_3038 → T_Setoid_46 Source #

du_setoid_3076 ∷ T_IsQuasigroup_3038 → T_Setoid_46 Source #

d_sym_3078 ∷ T_IsQuasigroup_3038 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_3080 ∷ T_IsQuasigroup_3038 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_3082 ∷ T_IsQuasigroup_3038 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_3084 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → T_IsQuasigroup_3038 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_3084 ∷ T_IsQuasigroup_3038 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_3086 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → T_IsQuasigroup_3038 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_3086 ∷ T_IsQuasigroup_3038 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'92''92''45'cong'737'_3088 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → T_IsQuasigroup_3038 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'92''92''45'cong'737'_3088 ∷ T_IsQuasigroup_3038 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'92''92''45'cong'691'_3092 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → T_IsQuasigroup_3038 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'92''92''45'cong'691'_3092 ∷ T_IsQuasigroup_3038 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'47''47''45'cong'737'_3096 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → T_IsQuasigroup_3038 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'47''47''45'cong'737'_3096 ∷ T_IsQuasigroup_3038 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'47''47''45'cong'691'_3100 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → T_IsQuasigroup_3038 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'47''47''45'cong'691'_3100 ∷ T_IsQuasigroup_3038 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_leftDivides'737'_3104 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → T_IsQuasigroup_3038 → AgdaAny → AgdaAny → AgdaAny Source #

du_leftDivides'737'_3104 ∷ T_IsQuasigroup_3038 → AgdaAny → AgdaAny → AgdaAny Source #

d_leftDivides'691'_3106 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → T_IsQuasigroup_3038 → AgdaAny → AgdaAny → AgdaAny Source #

du_leftDivides'691'_3106 ∷ T_IsQuasigroup_3038 → AgdaAny → AgdaAny → AgdaAny Source #

d_rightDivides'737'_3108 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → T_IsQuasigroup_3038 → AgdaAny → AgdaAny → AgdaAny Source #

du_rightDivides'737'_3108 ∷ T_IsQuasigroup_3038 → AgdaAny → AgdaAny → AgdaAny Source #

d_rightDivides'691'_3110 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → T_IsQuasigroup_3038 → AgdaAny → AgdaAny → AgdaAny Source #

du_rightDivides'691'_3110 ∷ T_IsQuasigroup_3038 → AgdaAny → AgdaAny → AgdaAny Source #

d_IsLoop_3122 ∷ p → p → p → p → p → p → p → p → () Source #

data T_IsLoop_3122 Source #

Constructors

C_constructor_3192 T_IsQuasigroup_3038 T_Σ_14

d_isQuasigroup_3136 ∷ T_IsLoop_3122 → T_IsQuasigroup_3038 Source #

d_identity_3138 ∷ T_IsLoop_3122 → T_Σ_14 Source #

d_'47''47''45'cong_3142 ∷ T_IsLoop_3122 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'47''47''45'cong'691'_3144 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsLoop_3122 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'47''47''45'cong'691'_3144 ∷ T_IsLoop_3122 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'47''47''45'cong'737'_3146 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsLoop_3122 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'47''47''45'cong'737'_3146 ∷ T_IsLoop_3122 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'92''92''45'cong_3148 ∷ T_IsLoop_3122 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'92''92''45'cong'691'_3150 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsLoop_3122 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'92''92''45'cong'691'_3150 ∷ T_IsLoop_3122 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'92''92''45'cong'737'_3152 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsLoop_3122 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'92''92''45'cong'737'_3152 ∷ T_IsLoop_3122 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_isEquivalence_3154 ∷ T_IsLoop_3122 → T_IsEquivalence_28 Source #

d_isMagma_3156 ∷ T_IsLoop_3122 → T_IsMagma_178 Source #

d_isPartialEquivalence_3158 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsLoop_3122 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_3158 ∷ T_IsLoop_3122 → T_IsPartialEquivalence_16 Source #

d_leftDivides_3160 ∷ T_IsLoop_3122 → T_Σ_14 Source #

d_leftDivides'691'_3162 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsLoop_3122 → AgdaAny → AgdaAny → AgdaAny Source #

du_leftDivides'691'_3162 ∷ T_IsLoop_3122 → AgdaAny → AgdaAny → AgdaAny Source #

d_leftDivides'737'_3164 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsLoop_3122 → AgdaAny → AgdaAny → AgdaAny Source #

du_leftDivides'737'_3164 ∷ T_IsLoop_3122 → AgdaAny → AgdaAny → AgdaAny Source #

d_refl_3166 ∷ T_IsLoop_3122 → AgdaAny → AgdaAny Source #

d_reflexive_3168 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsLoop_3122 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_3168 ∷ T_IsLoop_3122 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_rightDivides_3170 ∷ T_IsLoop_3122 → T_Σ_14 Source #

d_rightDivides'691'_3172 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsLoop_3122 → AgdaAny → AgdaAny → AgdaAny Source #

du_rightDivides'691'_3172 ∷ T_IsLoop_3122 → AgdaAny → AgdaAny → AgdaAny Source #

d_rightDivides'737'_3174 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsLoop_3122 → AgdaAny → AgdaAny → AgdaAny Source #

du_rightDivides'737'_3174 ∷ T_IsLoop_3122 → AgdaAny → AgdaAny → AgdaAny Source #

d_setoid_3176 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsLoop_3122 → T_Setoid_46 Source #

du_setoid_3176 ∷ T_IsLoop_3122 → T_Setoid_46 Source #

d_sym_3178 ∷ T_IsLoop_3122 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_3180 ∷ T_IsLoop_3122 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_3182 ∷ T_IsLoop_3122 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_3184 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsLoop_3122 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_3184 ∷ T_IsLoop_3122 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_3186 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsLoop_3122 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_3186 ∷ T_IsLoop_3122 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_identity'737'_3188 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsLoop_3122 → AgdaAny → AgdaAny Source #

du_identity'737'_3188 ∷ T_IsLoop_3122 → AgdaAny → AgdaAny Source #

d_identity'691'_3190 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsLoop_3122 → AgdaAny → AgdaAny Source #

du_identity'691'_3190 ∷ T_IsLoop_3122 → AgdaAny → AgdaAny Source #

d_IsLeftBolLoop_3202 ∷ p → p → p → p → p → p → p → p → () Source #

data T_IsLeftBolLoop_3202 Source #

Constructors

C_constructor_3276 T_IsLoop_3122 (AgdaAny → AgdaAny → AgdaAny → AgdaAny)

d_isLoop_3216 ∷ T_IsLeftBolLoop_3202 → T_IsLoop_3122 Source #

d_leftBol_3218 ∷ T_IsLeftBolLoop_3202 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'47''47''45'cong_3222 ∷ T_IsLeftBolLoop_3202 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'47''47''45'cong'691'_3224 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsLeftBolLoop_3202 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'47''47''45'cong'691'_3224 ∷ T_IsLeftBolLoop_3202 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'47''47''45'cong'737'_3226 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsLeftBolLoop_3202 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'47''47''45'cong'737'_3226 ∷ T_IsLeftBolLoop_3202 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'92''92''45'cong_3228 ∷ T_IsLeftBolLoop_3202 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'92''92''45'cong'691'_3230 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsLeftBolLoop_3202 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'92''92''45'cong'691'_3230 ∷ T_IsLeftBolLoop_3202 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'92''92''45'cong'737'_3232 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsLeftBolLoop_3202 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'92''92''45'cong'737'_3232 ∷ T_IsLeftBolLoop_3202 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_identity_3234 ∷ T_IsLeftBolLoop_3202 → T_Σ_14 Source #

d_identity'691'_3236 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsLeftBolLoop_3202 → AgdaAny → AgdaAny Source #

du_identity'691'_3236 ∷ T_IsLeftBolLoop_3202 → AgdaAny → AgdaAny Source #

d_identity'737'_3238 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsLeftBolLoop_3202 → AgdaAny → AgdaAny Source #

du_identity'737'_3238 ∷ T_IsLeftBolLoop_3202 → AgdaAny → AgdaAny Source #

d_isEquivalence_3240 ∷ T_IsLeftBolLoop_3202 → T_IsEquivalence_28 Source #

d_isMagma_3242 ∷ T_IsLeftBolLoop_3202 → T_IsMagma_178 Source #

d_isPartialEquivalence_3244 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsLeftBolLoop_3202 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_3244 ∷ T_IsLeftBolLoop_3202 → T_IsPartialEquivalence_16 Source #

d_isQuasigroup_3246 ∷ T_IsLeftBolLoop_3202 → T_IsQuasigroup_3038 Source #

d_leftDivides_3248 ∷ T_IsLeftBolLoop_3202 → T_Σ_14 Source #

d_leftDivides'691'_3250 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsLeftBolLoop_3202 → AgdaAny → AgdaAny → AgdaAny Source #

du_leftDivides'691'_3250 ∷ T_IsLeftBolLoop_3202 → AgdaAny → AgdaAny → AgdaAny Source #

d_leftDivides'737'_3252 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsLeftBolLoop_3202 → AgdaAny → AgdaAny → AgdaAny Source #

du_leftDivides'737'_3252 ∷ T_IsLeftBolLoop_3202 → AgdaAny → AgdaAny → AgdaAny Source #

d_refl_3254 ∷ T_IsLeftBolLoop_3202 → AgdaAny → AgdaAny Source #

d_reflexive_3256 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsLeftBolLoop_3202 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_3256 ∷ T_IsLeftBolLoop_3202 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_rightDivides_3258 ∷ T_IsLeftBolLoop_3202 → T_Σ_14 Source #

d_rightDivides'691'_3260 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsLeftBolLoop_3202 → AgdaAny → AgdaAny → AgdaAny Source #

du_rightDivides'691'_3260 ∷ T_IsLeftBolLoop_3202 → AgdaAny → AgdaAny → AgdaAny Source #

d_rightDivides'737'_3262 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsLeftBolLoop_3202 → AgdaAny → AgdaAny → AgdaAny Source #

du_rightDivides'737'_3262 ∷ T_IsLeftBolLoop_3202 → AgdaAny → AgdaAny → AgdaAny Source #

d_setoid_3264 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsLeftBolLoop_3202 → T_Setoid_46 Source #

du_setoid_3264 ∷ T_IsLeftBolLoop_3202 → T_Setoid_46 Source #

d_sym_3266 ∷ T_IsLeftBolLoop_3202 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_3268 ∷ T_IsLeftBolLoop_3202 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_3270 ∷ T_IsLeftBolLoop_3202 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_3272 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsLeftBolLoop_3202 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_3272 ∷ T_IsLeftBolLoop_3202 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_3274 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsLeftBolLoop_3202 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_3274 ∷ T_IsLeftBolLoop_3202 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_IsRightBolLoop_3286 ∷ p → p → p → p → p → p → p → p → () Source #

data T_IsRightBolLoop_3286 Source #

Constructors

C_constructor_3360 T_IsLoop_3122 (AgdaAny → AgdaAny → AgdaAny → AgdaAny)

d_isLoop_3300 ∷ T_IsRightBolLoop_3286 → T_IsLoop_3122 Source #

d_rightBol_3302 ∷ T_IsRightBolLoop_3286 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'47''47''45'cong_3306 ∷ T_IsRightBolLoop_3286 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'47''47''45'cong'691'_3308 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsRightBolLoop_3286 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'47''47''45'cong'691'_3308 ∷ T_IsRightBolLoop_3286 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'47''47''45'cong'737'_3310 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsRightBolLoop_3286 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'47''47''45'cong'737'_3310 ∷ T_IsRightBolLoop_3286 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'92''92''45'cong_3312 ∷ T_IsRightBolLoop_3286 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'92''92''45'cong'691'_3314 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsRightBolLoop_3286 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'92''92''45'cong'691'_3314 ∷ T_IsRightBolLoop_3286 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'92''92''45'cong'737'_3316 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsRightBolLoop_3286 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'92''92''45'cong'737'_3316 ∷ T_IsRightBolLoop_3286 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_identity_3318 ∷ T_IsRightBolLoop_3286 → T_Σ_14 Source #

d_identity'691'_3320 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsRightBolLoop_3286 → AgdaAny → AgdaAny Source #

du_identity'691'_3320 ∷ T_IsRightBolLoop_3286 → AgdaAny → AgdaAny Source #

d_identity'737'_3322 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsRightBolLoop_3286 → AgdaAny → AgdaAny Source #

du_identity'737'_3322 ∷ T_IsRightBolLoop_3286 → AgdaAny → AgdaAny Source #

d_isEquivalence_3324 ∷ T_IsRightBolLoop_3286 → T_IsEquivalence_28 Source #

d_isMagma_3326 ∷ T_IsRightBolLoop_3286 → T_IsMagma_178 Source #

d_isPartialEquivalence_3328 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsRightBolLoop_3286 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_3328 ∷ T_IsRightBolLoop_3286 → T_IsPartialEquivalence_16 Source #

d_isQuasigroup_3330 ∷ T_IsRightBolLoop_3286 → T_IsQuasigroup_3038 Source #

d_leftDivides_3332 ∷ T_IsRightBolLoop_3286 → T_Σ_14 Source #

d_leftDivides'691'_3334 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsRightBolLoop_3286 → AgdaAny → AgdaAny → AgdaAny Source #

du_leftDivides'691'_3334 ∷ T_IsRightBolLoop_3286 → AgdaAny → AgdaAny → AgdaAny Source #

d_leftDivides'737'_3336 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsRightBolLoop_3286 → AgdaAny → AgdaAny → AgdaAny Source #

du_leftDivides'737'_3336 ∷ T_IsRightBolLoop_3286 → AgdaAny → AgdaAny → AgdaAny Source #

d_refl_3338 ∷ T_IsRightBolLoop_3286 → AgdaAny → AgdaAny Source #

d_reflexive_3340 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsRightBolLoop_3286 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_3340 ∷ T_IsRightBolLoop_3286 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_rightDivides_3342 ∷ T_IsRightBolLoop_3286 → T_Σ_14 Source #

d_rightDivides'691'_3344 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsRightBolLoop_3286 → AgdaAny → AgdaAny → AgdaAny Source #

du_rightDivides'691'_3344 ∷ T_IsRightBolLoop_3286 → AgdaAny → AgdaAny → AgdaAny Source #

d_rightDivides'737'_3346 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsRightBolLoop_3286 → AgdaAny → AgdaAny → AgdaAny Source #

du_rightDivides'737'_3346 ∷ T_IsRightBolLoop_3286 → AgdaAny → AgdaAny → AgdaAny Source #

d_setoid_3348 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsRightBolLoop_3286 → T_Setoid_46 Source #

du_setoid_3348 ∷ T_IsRightBolLoop_3286 → T_Setoid_46 Source #

d_sym_3350 ∷ T_IsRightBolLoop_3286 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_3352 ∷ T_IsRightBolLoop_3286 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_3354 ∷ T_IsRightBolLoop_3286 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_3356 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsRightBolLoop_3286 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_3356 ∷ T_IsRightBolLoop_3286 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_3358 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsRightBolLoop_3286 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_3358 ∷ T_IsRightBolLoop_3286 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_IsMoufangLoop_3370 ∷ p → p → p → p → p → p → p → p → () Source #

data T_IsMoufangLoop_3370 Source #

Constructors

C_constructor_3452 T_IsLeftBolLoop_3202 (AgdaAny → AgdaAny → AgdaAny → AgdaAny) (AgdaAny → AgdaAny → AgdaAny → AgdaAny)

d_isLeftBolLoop_3386 ∷ T_IsMoufangLoop_3370 → T_IsLeftBolLoop_3202 Source #

d_rightBol_3388 ∷ T_IsMoufangLoop_3370 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_identical_3390 ∷ T_IsMoufangLoop_3370 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'47''47''45'cong_3394 ∷ T_IsMoufangLoop_3370 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'47''47''45'cong'691'_3396 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMoufangLoop_3370 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'47''47''45'cong'691'_3396 ∷ T_IsMoufangLoop_3370 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'47''47''45'cong'737'_3398 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMoufangLoop_3370 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'47''47''45'cong'737'_3398 ∷ T_IsMoufangLoop_3370 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'92''92''45'cong_3400 ∷ T_IsMoufangLoop_3370 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'92''92''45'cong'691'_3402 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMoufangLoop_3370 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'92''92''45'cong'691'_3402 ∷ T_IsMoufangLoop_3370 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'92''92''45'cong'737'_3404 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMoufangLoop_3370 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'92''92''45'cong'737'_3404 ∷ T_IsMoufangLoop_3370 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_identity_3406 ∷ T_IsMoufangLoop_3370 → T_Σ_14 Source #

d_identity'691'_3408 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMoufangLoop_3370 → AgdaAny → AgdaAny Source #

du_identity'691'_3408 ∷ T_IsMoufangLoop_3370 → AgdaAny → AgdaAny Source #

d_identity'737'_3410 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMoufangLoop_3370 → AgdaAny → AgdaAny Source #

du_identity'737'_3410 ∷ T_IsMoufangLoop_3370 → AgdaAny → AgdaAny Source #

d_isEquivalence_3412 ∷ T_IsMoufangLoop_3370 → T_IsEquivalence_28 Source #

d_isLoop_3414 ∷ T_IsMoufangLoop_3370 → T_IsLoop_3122 Source #

d_isMagma_3416 ∷ T_IsMoufangLoop_3370 → T_IsMagma_178 Source #

d_isPartialEquivalence_3418 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMoufangLoop_3370 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_3418 ∷ T_IsMoufangLoop_3370 → T_IsPartialEquivalence_16 Source #

d_isQuasigroup_3420 ∷ T_IsMoufangLoop_3370 → T_IsQuasigroup_3038 Source #

d_leftBol_3422 ∷ T_IsMoufangLoop_3370 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_leftDivides_3424 ∷ T_IsMoufangLoop_3370 → T_Σ_14 Source #

d_leftDivides'691'_3426 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMoufangLoop_3370 → AgdaAny → AgdaAny → AgdaAny Source #

du_leftDivides'691'_3426 ∷ T_IsMoufangLoop_3370 → AgdaAny → AgdaAny → AgdaAny Source #

d_leftDivides'737'_3428 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMoufangLoop_3370 → AgdaAny → AgdaAny → AgdaAny Source #

du_leftDivides'737'_3428 ∷ T_IsMoufangLoop_3370 → AgdaAny → AgdaAny → AgdaAny Source #

d_refl_3430 ∷ T_IsMoufangLoop_3370 → AgdaAny → AgdaAny Source #

d_reflexive_3432 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMoufangLoop_3370 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_3432 ∷ T_IsMoufangLoop_3370 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_rightDivides_3434 ∷ T_IsMoufangLoop_3370 → T_Σ_14 Source #

d_rightDivides'691'_3436 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMoufangLoop_3370 → AgdaAny → AgdaAny → AgdaAny Source #

du_rightDivides'691'_3436 ∷ T_IsMoufangLoop_3370 → AgdaAny → AgdaAny → AgdaAny Source #

d_rightDivides'737'_3438 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMoufangLoop_3370 → AgdaAny → AgdaAny → AgdaAny Source #

du_rightDivides'737'_3438 ∷ T_IsMoufangLoop_3370 → AgdaAny → AgdaAny → AgdaAny Source #

d_setoid_3440 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMoufangLoop_3370 → T_Setoid_46 Source #

du_setoid_3440 ∷ T_IsMoufangLoop_3370 → T_Setoid_46 Source #

d_sym_3442 ∷ T_IsMoufangLoop_3370 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_3444 ∷ T_IsMoufangLoop_3370 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_3446 ∷ T_IsMoufangLoop_3370 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_3448 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMoufangLoop_3370 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_3448 ∷ T_IsMoufangLoop_3370 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_3450 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMoufangLoop_3370 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_3450 ∷ T_IsMoufangLoop_3370 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_IsMiddleBolLoop_3462 ∷ p → p → p → p → p → p → p → p → () Source #

data T_IsMiddleBolLoop_3462 Source #

Constructors

C_constructor_3536 T_IsLoop_3122 (AgdaAny → AgdaAny → AgdaAny → AgdaAny)

d_isLoop_3476 ∷ T_IsMiddleBolLoop_3462 → T_IsLoop_3122 Source #

d_middleBol_3478 ∷ T_IsMiddleBolLoop_3462 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'47''47''45'cong_3482 ∷ T_IsMiddleBolLoop_3462 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'47''47''45'cong'691'_3484 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMiddleBolLoop_3462 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'47''47''45'cong'691'_3484 ∷ T_IsMiddleBolLoop_3462 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'47''47''45'cong'737'_3486 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMiddleBolLoop_3462 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'47''47''45'cong'737'_3486 ∷ T_IsMiddleBolLoop_3462 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'92''92''45'cong_3488 ∷ T_IsMiddleBolLoop_3462 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'92''92''45'cong'691'_3490 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMiddleBolLoop_3462 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'92''92''45'cong'691'_3490 ∷ T_IsMiddleBolLoop_3462 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'92''92''45'cong'737'_3492 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMiddleBolLoop_3462 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'92''92''45'cong'737'_3492 ∷ T_IsMiddleBolLoop_3462 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_identity_3494 ∷ T_IsMiddleBolLoop_3462 → T_Σ_14 Source #

d_identity'691'_3496 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMiddleBolLoop_3462 → AgdaAny → AgdaAny Source #

du_identity'691'_3496 ∷ T_IsMiddleBolLoop_3462 → AgdaAny → AgdaAny Source #

d_identity'737'_3498 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMiddleBolLoop_3462 → AgdaAny → AgdaAny Source #

du_identity'737'_3498 ∷ T_IsMiddleBolLoop_3462 → AgdaAny → AgdaAny Source #

d_isEquivalence_3500 ∷ T_IsMiddleBolLoop_3462 → T_IsEquivalence_28 Source #

d_isMagma_3502 ∷ T_IsMiddleBolLoop_3462 → T_IsMagma_178 Source #

d_isPartialEquivalence_3504 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMiddleBolLoop_3462 → T_IsPartialEquivalence_16 Source #

du_isPartialEquivalence_3504 ∷ T_IsMiddleBolLoop_3462 → T_IsPartialEquivalence_16 Source #

d_isQuasigroup_3506 ∷ T_IsMiddleBolLoop_3462 → T_IsQuasigroup_3038 Source #

d_leftDivides_3508 ∷ T_IsMiddleBolLoop_3462 → T_Σ_14 Source #

d_leftDivides'691'_3510 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMiddleBolLoop_3462 → AgdaAny → AgdaAny → AgdaAny Source #

du_leftDivides'691'_3510 ∷ T_IsMiddleBolLoop_3462 → AgdaAny → AgdaAny → AgdaAny Source #

d_leftDivides'737'_3512 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMiddleBolLoop_3462 → AgdaAny → AgdaAny → AgdaAny Source #

du_leftDivides'737'_3512 ∷ T_IsMiddleBolLoop_3462 → AgdaAny → AgdaAny → AgdaAny Source #

d_refl_3514 ∷ T_IsMiddleBolLoop_3462 → AgdaAny → AgdaAny Source #

d_reflexive_3516 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMiddleBolLoop_3462 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

du_reflexive_3516 ∷ T_IsMiddleBolLoop_3462 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #

d_rightDivides_3518 ∷ T_IsMiddleBolLoop_3462 → T_Σ_14 Source #

d_rightDivides'691'_3520 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMiddleBolLoop_3462 → AgdaAny → AgdaAny → AgdaAny Source #

du_rightDivides'691'_3520 ∷ T_IsMiddleBolLoop_3462 → AgdaAny → AgdaAny → AgdaAny Source #

d_rightDivides'737'_3522 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMiddleBolLoop_3462 → AgdaAny → AgdaAny → AgdaAny Source #

du_rightDivides'737'_3522 ∷ T_IsMiddleBolLoop_3462 → AgdaAny → AgdaAny → AgdaAny Source #

d_setoid_3524 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMiddleBolLoop_3462 → T_Setoid_46 Source #

du_setoid_3524 ∷ T_IsMiddleBolLoop_3462 → T_Setoid_46 Source #

d_sym_3526 ∷ T_IsMiddleBolLoop_3462 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_trans_3528 ∷ T_IsMiddleBolLoop_3462 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong_3530 ∷ T_IsMiddleBolLoop_3462 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'691'_3532 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMiddleBolLoop_3462 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'691'_3532 ∷ T_IsMiddleBolLoop_3462 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

d_'8729''45'cong'737'_3534 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMiddleBolLoop_3462 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #

du_'8729''45'cong'737'_3534 ∷ T_IsMiddleBolLoop_3462 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #