| Safe Haskell | Safe-Inferred |
|---|---|
| Language | Haskell2010 |
MAlonzo.Code.Algebra.Structures.Biased
Documentation
d__DistributesOver__18 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → () Source #
d__DistributesOver'691'__20 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → () Source #
d__DistributesOver'737'__22 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → () Source #
d_Commutative_42 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → () Source #
d_LeftIdentity_84 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → AgdaAny → (AgdaAny → AgdaAny → AgdaAny) → () Source #
d_LeftZero_92 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → AgdaAny → (AgdaAny → AgdaAny → AgdaAny) → () Source #
d_RightIdentity_114 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → AgdaAny → (AgdaAny → AgdaAny → AgdaAny) → () Source #
d_RightZero_122 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → AgdaAny → (AgdaAny → AgdaAny → AgdaAny) → () Source #
d_Zero_142 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → AgdaAny → (AgdaAny → AgdaAny → AgdaAny) → () Source #
d_IsAbelianGroup_146 ∷ p → p → p → p → p → p → p → () Source #
d_IsCommutativeMonoid_170 ∷ p → p → p → p → p → p → () Source #
d_IsCommutativeSemiring_182 ∷ p → p → p → p → p → p → p → p → () Source #
d_IsMonoid_246 ∷ p → p → p → p → p → p → () Source #
d_IsNearSemiring_254 ∷ p → p → p → p → p → p → p → () Source #
d_IsRing_278 ∷ p → p → p → p → p → p → p → p → p → () Source #
d_IsSemigroup_290 ∷ p → p → p → p → p → () Source #
d_IsSemiringWithoutAnnihilatingZero_302 ∷ p → p → p → p → p → p → p → p → () Source #
d_IsSemiringWithoutOne_306 ∷ p → p → p → p → p → p → p → () Source #
d__'47''47'__320 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsAbelianGroup_1172 → AgdaAny → AgdaAny → AgdaAny Source #
du__'47''47'__320 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → AgdaAny Source #
d_identity'691'_328 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsAbelianGroup_1172 → AgdaAny → AgdaAny Source #
d_identity'737'_330 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsAbelianGroup_1172 → AgdaAny → AgdaAny Source #
d_inverse'691'_334 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsAbelianGroup_1172 → AgdaAny → AgdaAny Source #
d_inverse'737'_336 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsAbelianGroup_1172 → AgdaAny → AgdaAny Source #
d_isCommutativeMagma_338 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsAbelianGroup_1172 → T_IsCommutativeMagma_214 Source #
d_isCommutativeMonoid_340 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsAbelianGroup_1172 → T_IsCommutativeMonoid_764 Source #
du_isCommutativeMonoid_340 ∷ (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsAbelianGroup_1172 → T_IsCommutativeMonoid_764 Source #
d_isCommutativeSemigroup_342 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsAbelianGroup_1172 → T_IsCommutativeSemigroup_568 Source #
d_isInvertibleMagma_348 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsAbelianGroup_1172 → T_IsInvertibleMagma_958 Source #
d_isInvertibleUnitalMagma_350 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsAbelianGroup_1172 → T_IsInvertibleUnitalMagma_1012 Source #
d_isPartialEquivalence_356 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsAbelianGroup_1172 → T_IsPartialEquivalence_16 Source #
d_isUnitalMagma_360 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsAbelianGroup_1172 → T_IsUnitalMagma_666 Source #
d_reflexive_364 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsAbelianGroup_1172 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #
d_setoid_366 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsAbelianGroup_1172 → T_Setoid_46 Source #
d_unique'691''45''8315''185'_372 ∷ 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'_372 ∷ (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsAbelianGroup_1172 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
d_unique'737''45''8315''185'_374 ∷ 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'_374 ∷ (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → (AgdaAny → AgdaAny) → T_IsAbelianGroup_1172 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
d_'8729''45'cong'691'_380 ∷ 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'_380 ∷ T_IsAbelianGroup_1172 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
d_'8729''45'cong'737'_382 ∷ 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'_382 ∷ T_IsAbelianGroup_1172 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
d_identity'691'_1698 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMonoid_712 → AgdaAny → AgdaAny Source #
du_identity'691'_1698 ∷ (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMonoid_712 → AgdaAny → AgdaAny Source #
d_identity'737'_1700 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMonoid_712 → AgdaAny → AgdaAny Source #
du_identity'737'_1700 ∷ (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMonoid_712 → AgdaAny → AgdaAny Source #
d_isPartialEquivalence_1706 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMonoid_712 → T_IsPartialEquivalence_16 Source #
d_isUnitalMagma_1710 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMonoid_712 → T_IsUnitalMagma_666 Source #
du_isUnitalMagma_1710 ∷ (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMonoid_712 → T_IsUnitalMagma_666 Source #
d_reflexive_1714 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMonoid_712 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #
d_setoid_1716 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsMonoid_712 → T_Setoid_46 Source #
d_'8729''45'cong'691'_1724 ∷ 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'_1724 ∷ T_IsMonoid_712 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
d_'8729''45'cong'737'_1726 ∷ 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'_1726 ∷ T_IsMonoid_712 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
d_'42''45'cong_1798 ∷ T_IsNearSemiring_1260 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
d_'42''45'assoc_2214 ∷ T_IsRing_2740 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
d_'42''45'cong_2216 ∷ T_IsRing_2740 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
d_assoc_2442 ∷ T_IsSemigroup_488 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
d_'42''45'assoc_2582 ∷ T_IsSemiringWithoutAnnihilatingZero_1536 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
d_'42''45'cong_2584 ∷ T_IsSemiringWithoutAnnihilatingZero_1536 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
d_'43''45'isCommutativeMonoid_2620 ∷ T_IsSemiringWithoutAnnihilatingZero_1536 → T_IsCommutativeMonoid_764 Source #
d_'42''45'cong_2656 ∷ T_IsSemiringWithoutOne_1342 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
d_'43''45'isCommutativeMonoid_2684 ∷ T_IsSemiringWithoutOne_1342 → T_IsCommutativeMonoid_764 Source #
d_IsCommutativeMonoid'737'_2770 ∷ p → p → p → p → p → p → () Source #
data T_IsCommutativeMonoid'737'_2770 Source #
Constructors
| C_constructor_2820 T_IsSemigroup_488 (AgdaAny → AgdaAny) (AgdaAny → AgdaAny → AgdaAny) |
d_isCommutativeMonoid_2788 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeMonoid'737'_2770 → T_IsCommutativeMonoid_764 Source #
du_isCommutativeMonoid_2788 ∷ (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeMonoid'737'_2770 → T_IsCommutativeMonoid_764 Source #
d_IsCommutativeMonoid'691'_2826 ∷ p → p → p → p → p → p → () Source #
data T_IsCommutativeMonoid'691'_2826 Source #
Constructors
| C_constructor_2876 T_IsSemigroup_488 (AgdaAny → AgdaAny) (AgdaAny → AgdaAny → AgdaAny) |
d_isCommutativeMonoid_2844 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeMonoid'691'_2826 → T_IsCommutativeMonoid_764 Source #
du_isCommutativeMonoid_2844 ∷ (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeMonoid'691'_2826 → T_IsCommutativeMonoid_764 Source #
d_IsSemiringWithoutOne'42'_2884 ∷ p → p → p → p → p → p → p → () Source #
d_'43''45'isCommutativeMonoid_2900 ∷ T_IsSemiringWithoutOne'42'_2884 → T_IsCommutativeMonoid_764 Source #
d_isSemiringWithoutOne_2908 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsSemiringWithoutOne'42'_2884 → T_IsSemiringWithoutOne_1342 Source #
du_isSemiringWithoutOne_2908 ∷ T_IsSemiringWithoutOne'42'_2884 → T_IsSemiringWithoutOne_1342 Source #
d_IsNearSemiring'42'_2948 ∷ p → p → p → p → p → p → p → () Source #
data T_IsNearSemiring'42'_2948 Source #
Constructors
| C_constructor_3004 T_IsMonoid_712 T_IsSemigroup_488 (AgdaAny → AgdaAny → AgdaAny → AgdaAny) (AgdaAny → AgdaAny) |
d_isNearSemiring_2972 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsNearSemiring'42'_2948 → T_IsNearSemiring_1260 Source #
d_IsSemiringWithoutAnnihilatingZero'42'_3014 ∷ p → p → p → p → p → p → p → p → () Source #
d_'43''45'isCommutativeMonoid_3030 ∷ T_IsSemiringWithoutAnnihilatingZero'42'_3014 → T_IsCommutativeMonoid_764 Source #
d_isSemiringWithoutAnnihilatingZero_3036 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiringWithoutAnnihilatingZero'42'_3014 → T_IsSemiringWithoutAnnihilatingZero_1536 Source #
du_isSemiringWithoutAnnihilatingZero_3036 ∷ T_IsSemiringWithoutAnnihilatingZero'42'_3014 → T_IsSemiringWithoutAnnihilatingZero_1536 Source #
d_identity'691'_3048 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiringWithoutAnnihilatingZero'42'_3014 → AgdaAny → AgdaAny Source #
d_identity'737'_3050 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiringWithoutAnnihilatingZero'42'_3014 → AgdaAny → AgdaAny Source #
d_isPartialEquivalence_3056 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiringWithoutAnnihilatingZero'42'_3014 → T_IsPartialEquivalence_16 Source #
du_isPartialEquivalence_3056 ∷ T_IsSemiringWithoutAnnihilatingZero'42'_3014 → T_IsPartialEquivalence_16 Source #
d_isUnitalMagma_3060 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiringWithoutAnnihilatingZero'42'_3014 → T_IsUnitalMagma_666 Source #
d_reflexive_3064 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiringWithoutAnnihilatingZero'42'_3014 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #
du_reflexive_3064 ∷ T_IsSemiringWithoutAnnihilatingZero'42'_3014 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #
d_setoid_3066 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiringWithoutAnnihilatingZero'42'_3014 → T_Setoid_46 Source #
d_'8729''45'cong'691'_3074 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiringWithoutAnnihilatingZero'42'_3014 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
du_'8729''45'cong'691'_3074 ∷ T_IsSemiringWithoutAnnihilatingZero'42'_3014 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
d_'8729''45'cong'737'_3076 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsSemiringWithoutAnnihilatingZero'42'_3014 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
du_'8729''45'cong'737'_3076 ∷ T_IsSemiringWithoutAnnihilatingZero'42'_3014 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
d_IsCommutativeSemiring'737'_3088 ∷ p → p → p → p → p → p → p → p → () Source #
data T_IsCommutativeSemiring'737'_3088 Source #
Constructors
| C_constructor_3208 T_IsCommutativeMonoid_764 T_IsCommutativeMonoid_764 (AgdaAny → AgdaAny → AgdaAny → AgdaAny) (AgdaAny → AgdaAny) |
d_'43''45'isCommutativeMonoid_3106 ∷ T_IsCommutativeSemiring'737'_3088 → T_IsCommutativeMonoid_764 Source #
d_'42''45'isCommutativeMonoid_3108 ∷ T_IsCommutativeSemiring'737'_3088 → T_IsCommutativeMonoid_764 Source #
d_distrib'691'_3110 ∷ T_IsCommutativeSemiring'737'_3088 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
d_isCommutativeSemiring_3114 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeSemiring'737'_3088 → T_IsCommutativeSemiring_1750 Source #
du_isCommutativeSemiring_3114 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeSemiring'737'_3088 → T_IsCommutativeSemiring_1750 Source #
d_IsCommutativeSemiring'691'_3218 ∷ p → p → p → p → p → p → p → p → () Source #
data T_IsCommutativeSemiring'691'_3218 Source #
Constructors
| C_constructor_3338 T_IsCommutativeMonoid_764 T_IsCommutativeMonoid_764 (AgdaAny → AgdaAny → AgdaAny → AgdaAny) (AgdaAny → AgdaAny) |
d_'43''45'isCommutativeMonoid_3236 ∷ T_IsCommutativeSemiring'691'_3218 → T_IsCommutativeMonoid_764 Source #
d_'42''45'isCommutativeMonoid_3238 ∷ T_IsCommutativeSemiring'691'_3218 → T_IsCommutativeMonoid_764 Source #
d_distrib'737'_3240 ∷ T_IsCommutativeSemiring'691'_3218 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
d_isCommutativeSemiring_3244 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsCommutativeSemiring'691'_3218 → T_IsCommutativeSemiring_1750 Source #
du_isCommutativeSemiring_3244 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → AgdaAny → T_IsCommutativeSemiring'691'_3218 → T_IsCommutativeSemiring_1750 Source #
d_IsRing'42'_3350 ∷ p → p → p → p → p → p → p → p → p → () Source #
data T_IsRing'42'_3350 Source #
d_isRing_3378 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing'42'_3350 → T_IsRing_2740 Source #
d_identity'691'_3390 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing'42'_3350 → AgdaAny → AgdaAny Source #
d_identity'737'_3392 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing'42'_3350 → AgdaAny → AgdaAny Source #
d_isPartialEquivalence_3398 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing'42'_3350 → T_IsPartialEquivalence_16 Source #
d_isUnitalMagma_3402 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing'42'_3350 → T_IsUnitalMagma_666 Source #
d_reflexive_3406 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing'42'_3350 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #
d_setoid_3408 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing'42'_3350 → T_Setoid_46 Source #
d_'8729''45'cong'691'_3416 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing'42'_3350 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
du_'8729''45'cong'691'_3416 ∷ T_IsRing'42'_3350 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
d_'8729''45'cong'737'_3418 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRing'42'_3350 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
du_'8729''45'cong'737'_3418 ∷ T_IsRing'42'_3350 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
d_IsRingWithoutAnnihilatingZero_3432 ∷ p → p → p → p → p → p → p → p → p → () Source #
data T_IsRingWithoutAnnihilatingZero_3432 Source #
Constructors
| C_constructor_3566 T_IsAbelianGroup_1172 T_IsMonoid_712 T_Σ_14 |
d_'43''45'isAbelianGroup_3450 ∷ T_IsRingWithoutAnnihilatingZero_3432 → T_IsAbelianGroup_1172 Source #
d__'47''47'__3458 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRingWithoutAnnihilatingZero_3432 → AgdaAny → AgdaAny → AgdaAny Source #
du__'47''47'__3458 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → AgdaAny Source #
d_assoc_3460 ∷ T_IsRingWithoutAnnihilatingZero_3432 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
d_identity'691'_3466 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRingWithoutAnnihilatingZero_3432 → AgdaAny → AgdaAny Source #
d_identity'737'_3468 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRingWithoutAnnihilatingZero_3432 → AgdaAny → AgdaAny Source #
d_inverse'691'_3472 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRingWithoutAnnihilatingZero_3432 → AgdaAny → AgdaAny Source #
d_inverse'737'_3474 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRingWithoutAnnihilatingZero_3432 → AgdaAny → AgdaAny Source #
d_isCommutativeMagma_3476 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRingWithoutAnnihilatingZero_3432 → T_IsCommutativeMagma_214 Source #
du_isCommutativeMagma_3476 ∷ T_IsRingWithoutAnnihilatingZero_3432 → T_IsCommutativeMagma_214 Source #
d_isCommutativeMonoid_3478 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRingWithoutAnnihilatingZero_3432 → T_IsCommutativeMonoid_764 Source #
du_isCommutativeMonoid_3478 ∷ T_IsRingWithoutAnnihilatingZero_3432 → T_IsCommutativeMonoid_764 Source #
d_isCommutativeSemigroup_3480 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRingWithoutAnnihilatingZero_3432 → T_IsCommutativeSemigroup_568 Source #
du_isCommutativeSemigroup_3480 ∷ T_IsRingWithoutAnnihilatingZero_3432 → T_IsCommutativeSemigroup_568 Source #
d_isInvertibleMagma_3486 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRingWithoutAnnihilatingZero_3432 → T_IsInvertibleMagma_958 Source #
d_isInvertibleUnitalMagma_3488 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRingWithoutAnnihilatingZero_3432 → T_IsInvertibleUnitalMagma_1012 Source #
du_isInvertibleUnitalMagma_3488 ∷ T_IsRingWithoutAnnihilatingZero_3432 → T_IsInvertibleUnitalMagma_1012 Source #
d_isPartialEquivalence_3494 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRingWithoutAnnihilatingZero_3432 → T_IsPartialEquivalence_16 Source #
du_isPartialEquivalence_3494 ∷ T_IsRingWithoutAnnihilatingZero_3432 → T_IsPartialEquivalence_16 Source #
d_isUnitalMagma_3498 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRingWithoutAnnihilatingZero_3432 → T_IsUnitalMagma_666 Source #
d_reflexive_3502 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRingWithoutAnnihilatingZero_3432 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #
du_reflexive_3502 ∷ T_IsRingWithoutAnnihilatingZero_3432 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #
d_setoid_3504 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRingWithoutAnnihilatingZero_3432 → T_Setoid_46 Source #
d_trans_3508 ∷ T_IsRingWithoutAnnihilatingZero_3432 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
d_unique'691''45''8315''185'_3510 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRingWithoutAnnihilatingZero_3432 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
du_unique'691''45''8315''185'_3510 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutAnnihilatingZero_3432 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
d_unique'737''45''8315''185'_3512 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRingWithoutAnnihilatingZero_3432 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
du_unique'737''45''8315''185'_3512 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutAnnihilatingZero_3432 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
d_'8315''185''45'cong_3514 ∷ T_IsRingWithoutAnnihilatingZero_3432 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
d_'8729''45'cong_3516 ∷ T_IsRingWithoutAnnihilatingZero_3432 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
d_'8729''45'cong'691'_3518 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRingWithoutAnnihilatingZero_3432 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
du_'8729''45'cong'691'_3518 ∷ T_IsRingWithoutAnnihilatingZero_3432 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
d_'8729''45'cong'737'_3520 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRingWithoutAnnihilatingZero_3432 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
du_'8729''45'cong'737'_3520 ∷ T_IsRingWithoutAnnihilatingZero_3432 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
d_assoc_3524 ∷ T_IsRingWithoutAnnihilatingZero_3432 → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
d_identity'691'_3528 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRingWithoutAnnihilatingZero_3432 → AgdaAny → AgdaAny Source #
d_identity'737'_3530 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRingWithoutAnnihilatingZero_3432 → AgdaAny → AgdaAny Source #
d_isPartialEquivalence_3536 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRingWithoutAnnihilatingZero_3432 → T_IsPartialEquivalence_16 Source #
du_isPartialEquivalence_3536 ∷ T_IsRingWithoutAnnihilatingZero_3432 → T_IsPartialEquivalence_16 Source #
d_isUnitalMagma_3540 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRingWithoutAnnihilatingZero_3432 → T_IsUnitalMagma_666 Source #
d_reflexive_3544 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRingWithoutAnnihilatingZero_3432 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #
du_reflexive_3544 ∷ T_IsRingWithoutAnnihilatingZero_3432 → AgdaAny → AgdaAny → T__'8801'__12 → AgdaAny Source #
d_setoid_3546 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRingWithoutAnnihilatingZero_3432 → T_Setoid_46 Source #
d_trans_3550 ∷ T_IsRingWithoutAnnihilatingZero_3432 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
d_'8729''45'cong_3552 ∷ T_IsRingWithoutAnnihilatingZero_3432 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
d_'8729''45'cong'691'_3554 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRingWithoutAnnihilatingZero_3432 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
du_'8729''45'cong'691'_3554 ∷ T_IsRingWithoutAnnihilatingZero_3432 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
d_'8729''45'cong'737'_3556 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRingWithoutAnnihilatingZero_3432 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
du_'8729''45'cong'737'_3556 ∷ T_IsRingWithoutAnnihilatingZero_3432 → AgdaAny → AgdaAny → AgdaAny → AgdaAny → AgdaAny Source #
d_zero'737'_3558 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRingWithoutAnnihilatingZero_3432 → AgdaAny → AgdaAny Source #
du_zero'737'_3558 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutAnnihilatingZero_3432 → AgdaAny → AgdaAny Source #
d_zero'691'_3560 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRingWithoutAnnihilatingZero_3432 → AgdaAny → AgdaAny Source #
du_zero'691'_3560 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutAnnihilatingZero_3432 → AgdaAny → AgdaAny Source #
d_zero_3562 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRingWithoutAnnihilatingZero_3432 → T_Σ_14 Source #
du_zero_3562 ∷ (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → T_IsRingWithoutAnnihilatingZero_3432 → T_Σ_14 Source #
d_isRing_3564 ∷ T_Level_18 → T_Level_18 → () → (AgdaAny → AgdaAny → ()) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny → AgdaAny) → (AgdaAny → AgdaAny) → AgdaAny → AgdaAny → T_IsRingWithoutAnnihilatingZero_3432 → T_IsRing_2740 Source #