Search is not available for this dataset
fact
string | imports
string | filename
string | symbolic_name
string | __index_level_0__
int64 |
|---|---|---|---|---|
Definition singleton {A : Type} (x : key) (v : A) : t A (Dom.singleton x) := exist (OK (Dom.singleton x)) (S.add x v (@S.empty A)) (singleton_OK x v).
|
Utf8 MSets FMaps Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapImplementation
|
coq-contribs-dep-map
| 836 |
Definition remove {A : Type} {dom : Dom.t} (x : key) (m : @t A dom) : @t A (Dom.remove x dom) := exist (OK (Dom.remove x dom)) (S.remove x (proj1_sig m)) (remove_OK x m).
|
Utf8 MSets FMaps Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapImplementation
|
coq-contribs-dep-map
| 837 |
Definition constant (A : Type) dom (v : A) : t A dom := exist (OK dom) (Dom.fold (fun x m => S.add x v m) dom (@S.empty A)) (constant_OK dom v).
|
Utf8 MSets FMaps Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapImplementation
|
coq-contribs-dep-map
| 838 |
Definition fold {A B : Type} (f : key -> A -> B -> B) dom (m : t A dom) (i : B) : B := S.fold f (proj1_sig m) i.
|
Utf8 MSets FMaps Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapImplementation
|
coq-contribs-dep-map
| 839 |
Definition map {A B : Type} (f : A -> B) dom (m : t A dom) : t B dom := exist (OK dom) (S.map f (proj1_sig m)) (map_OK f m).
|
Utf8 MSets FMaps Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapImplementation
|
coq-contribs-dep-map
| 840 |
Definition Scombine {A B C : Type} (f : A -> B -> C) (g : A -> C) (h : B -> C) (m₁ : S.t A) (m₂ : S.t B) : S.t C := Dom.fold (fun x acc => match S.find x m₁, S.find x m₂ with | Some v₁, Some v₂ => S.add x (f v₁ v₂) acc | Some v, None => S.add x (g v) acc | None, Some v => S.add x (h v) acc | None, None => acc end) (Dom.union (S.fold (fun x _ acc => Dom.add x acc) m₁ Dom.empty) (S.fold (fun x _ acc => Dom.add x acc) m₂ Dom.empty)) (S.empty C).
|
Utf8 MSets FMaps Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapImplementation
|
coq-contribs-dep-map
| 841 |
Definition combine A B C f g₁ g₂ dom₁ dom₂ (m₁ : t A dom₁) (m₂ : t B dom₂) : t C (Dom.union dom₁ dom₂) := exist (OK (Dom.union dom₁ dom₂)) (Scombine f g₁ g₂ (proj1_sig m₁) (proj1_sig m₂)) (combine_OK f g₁ g₂ m₁ m₂).
|
Utf8 MSets FMaps Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapImplementation
|
coq-contribs-dep-map
| 842 |
Definition cast {A : Type} dom₁ dom₂ (Heq : Dom.eq dom₁ dom₂) (m : t A dom₁) : t A dom₂ := exist (OK dom₂) (proj1_sig m) (cast_OK Heq (proj2_sig m)).
|
Utf8 MSets FMaps Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapImplementation
|
coq-contribs-dep-map
| 843 |
Definition elements A dom (m : t A dom) := S.elements (proj1_sig m).
|
Utf8 MSets FMaps Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapImplementation
|
coq-contribs-dep-map
| 844 |
Definition from_elements A (l : list (key * A)) : t A (List.fold_left (fun acc xv => Dom.add (fst xv) acc) l Dom.empty) := exist (OK (List.fold_left (fun acc xv => Dom.add (fst xv) acc) l Dom.empty)) (List.fold_left (fun acc xv => S.add (fst xv) (snd xv) acc) l (@S.empty A)) (from_elements_OK l).
|
Utf8 MSets FMaps Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapImplementation
|
coq-contribs-dep-map
| 845 |
Definition full_relation {A : Type} : relation A := fun x y : A => True.
|
SetoidList Orders
|
coq-contribs-dep-map/Coqlib
|
coq-contribs-dep-map
| 846 |
Definition t := O.t.
|
SetoidList Orders
|
coq-contribs-dep-map/Coqlib
|
coq-contribs-dep-map
| 847 |
Definition eq := O.eq.
|
SetoidList Orders
|
coq-contribs-dep-map/Coqlib
|
coq-contribs-dep-map
| 848 |
Definition lt := O.lt.
|
SetoidList Orders
|
coq-contribs-dep-map/Coqlib
|
coq-contribs-dep-map
| 849 |
Definition eq_refl : forall x, eq x x := reflexivity.
|
SetoidList Orders
|
coq-contribs-dep-map/Coqlib
|
coq-contribs-dep-map
| 850 |
Definition eq_dec := O.eq_dec.
|
SetoidList Orders
|
coq-contribs-dep-map/Coqlib
|
coq-contribs-dep-map
| 851 |
Definition eq {A : Type} {dom₁ dom₂} (m₁ : t A dom₁) (m₂ : t A dom₂) := forall x, find x m₁ = find x m₂.
|
Utf8 Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapFactsInterface
|
coq-contribs-dep-map
| 852 |
Definition incl {A : Type} {dom₁ dom₂} (m₁ : t A dom₁) (m₂ : t A dom₂) := forall x v, find x m₁ = Some v -> find x m₂ = Some v.
|
Utf8 Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapFactsInterface
|
coq-contribs-dep-map
| 853 |
Parameter eq_sym : forall A dom₁ dom₂ (m₁ : t A dom₁) (m₂ : t A dom₂), eq m₁ m₂ -> eq m₂ m₁.
|
Utf8 Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapFactsInterface
|
coq-contribs-dep-map
| 854 |
Parameter eq_trans : forall A dom₁ dom₂ dom3 (m₁ : t A dom₁) (m₂ : t A dom₂) (m3 : t A dom3), eq m₁ m₂ -> eq m₂ m3 -> eq m₁ m3.
|
Utf8 Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapFactsInterface
|
coq-contribs-dep-map
| 855 |
Parameter incl_trans : forall A dom₁ dom₂ dom3 (m₁ : t A dom₁) (m₂ : t A dom₂) (m3 : t A dom3), incl m₁ m₂ -> incl m₂ m3 -> incl m₁ m3.
|
Utf8 Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapFactsInterface
|
coq-contribs-dep-map
| 856 |
Parameter find_compat : forall A x y dom₁ dom₂ (m₁ : t A dom₁) (m₂ : t A dom₂), X.eq x y -> eq m₁ m₂ -> find x m₁ = find y m₂.
|
Utf8 Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapFactsInterface
|
coq-contribs-dep-map
| 857 |
Parameter set_compat : forall A x y v dom₁ dom₂ (m₁ : t A dom₁) (m₂ : t A dom₂) (Hin₁ : Dom.In x dom₁) (Hin₂ : Dom.In y dom₂), X.eq x y -> eq m₁ m₂ -> eq (set x v m₁ Hin₁) (set y v m₂ Hin₂).
|
Utf8 Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapFactsInterface
|
coq-contribs-dep-map
| 858 |
Parameter add_compat : forall A x y v dom₁ dom₂ (m₁ : t A dom₁) (m₂ : t A dom₂), X.eq x y -> eq m₁ m₂ -> eq (add x v m₁) (add y v m₂).
|
Utf8 Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapFactsInterface
|
coq-contribs-dep-map
| 859 |
Parameter remove_compat : forall A x y dom₁ dom₂ (m₁ : t A dom₁) (m₂ : t A dom₂), X.eq x y -> eq m₁ m₂ -> eq (remove x m₁) (remove y m₂).
|
Utf8 Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapFactsInterface
|
coq-contribs-dep-map
| 860 |
Parameter find_None : forall A dom x (m : t A dom), find x m = None <-> ¬Dom.In x dom.
|
Utf8 Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapFactsInterface
|
coq-contribs-dep-map
| 861 |
Parameter find_dom : forall A x v dom (m : t A dom), find x m = Some v -> Dom.In x dom.
|
Utf8 Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapFactsInterface
|
coq-contribs-dep-map
| 862 |
Parameter set_Some : forall A x y v u dom (m : t A dom) (Hin : Dom.In x dom), find y (set x v m Hin) = Some u <-> X.eq y x ∧ u = v ∨ ¬X.eq y x ∧ find y m = Some u.
|
Utf8 Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapFactsInterface
|
coq-contribs-dep-map
| 863 |
Parameter set_None : forall A x y v dom (m : t A dom) (Hin : Dom.In x dom), find y (set x v m Hin) = None <-> ¬X.eq y x ∧ find y m = None.
|
Utf8 Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapFactsInterface
|
coq-contribs-dep-map
| 864 |
Parameter add_Some : forall A x y v u dom (m : t A dom), find y (add x v m) = Some u <-> X.eq y x ∧ u = v ∨ ¬X.eq y x ∧ find y m = Some u.
|
Utf8 Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapFactsInterface
|
coq-contribs-dep-map
| 865 |
Parameter add_None : forall A x y v dom (m : t A dom), find y (add x v m) = None <-> ¬X.eq y x ∧ find y m = None.
|
Utf8 Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapFactsInterface
|
coq-contribs-dep-map
| 866 |
Parameter remove_Some : forall A x y u dom (m : t A dom), find y (remove x m) = Some u <-> ¬X.eq y x ∧ find y m = Some u.
|
Utf8 Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapFactsInterface
|
coq-contribs-dep-map
| 867 |
Parameter remove_None : forall A x y dom (m : t A dom), find y (remove x m) = None <-> X.eq y x ∨ find y m = None.
|
Utf8 Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapFactsInterface
|
coq-contribs-dep-map
| 868 |
Parameter add_cancel : forall A x v dom (m : t A dom), find x m = Some v -> eq (add x v m) m.
|
Utf8 Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapFactsInterface
|
coq-contribs-dep-map
| 869 |
Parameter remove_cancel : forall A x dom (m : t A dom), find x m = None -> eq (remove x m) m.
|
Utf8 Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapFactsInterface
|
coq-contribs-dep-map
| 870 |
Parameter add_merge : forall A x v₁ v₂ dom (m : t A dom), eq (add x v₂ (add x v₁ m)) (add x v₂ m).
|
Utf8 Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapFactsInterface
|
coq-contribs-dep-map
| 871 |
Parameter add_comm : forall A x y v₁ v₂ dom (m : t A dom), ¬X.eq x y -> eq (add y v₂ (add x v₁ m)) (add x v₁ (add y v₂ m)).
|
Utf8 Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapFactsInterface
|
coq-contribs-dep-map
| 872 |
Parameter remove_add_cancel : forall A s v dom (m : t A dom), eq (remove s (add s v m)) (remove s m).
|
Utf8 Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapFactsInterface
|
coq-contribs-dep-map
| 873 |
Parameter map_None : forall A B (f : A -> B) dom (m : t A dom) x, find x (map f m) = None <-> ¬Dom.In x dom.
|
Utf8 Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapFactsInterface
|
coq-contribs-dep-map
| 874 |
Parameter combine_None : forall A B C (f : A -> B -> C) g₁ g₂ dom₁ dom₂ (m₁ : t A dom₁) (m₂ : t B dom₂) x, find x (combine f g₁ g₂ m₁ m₂) = None <-> find x m₁ = None ∧ find x m₂ = None.
|
Utf8 Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapFactsInterface
|
coq-contribs-dep-map
| 875 |
Parameter add_incl : forall A x v dom (m : t A dom), ¬Dom.In x dom -> incl m (add x v m).
|
Utf8 Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapFactsInterface
|
coq-contribs-dep-map
| 876 |
Parameter remove_incl : forall A x dom (m : t A dom), incl (remove x m) m.
|
Utf8 Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapFactsInterface
|
coq-contribs-dep-map
| 877 |
Parameter cast_spec : forall A dom₁ dom₂ (Heq : Dom.eq dom₁ dom₂) (m : t A dom₁), eq (cast Heq m) m.
|
Utf8 Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapFactsInterface
|
coq-contribs-dep-map
| 878 |
Parameter eq_dom : forall A dom₁ dom₂ (m₁ : t A dom₁) (m₂ : t A dom₂), eq m₁ m₂ -> Dom.eq dom₁ dom₂.
|
Utf8 Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapFactsInterface
|
coq-contribs-dep-map
| 879 |
Parameter for_all : forall {A}, (key -> A -> bool) -> forall {dom}, t A dom -> bool.
|
Utf8 Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapFactsInterface
|
coq-contribs-dep-map
| 880 |
Parameter for_all_spec : forall A f, Proper (X.eq ==> Logic.eq ==> Logic.eq) f -> forall dom (m : t A dom), for_all f m = true <-> forall x v, find x m = Some v -> f x v = true.
|
Utf8 Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapFactsInterface
|
coq-contribs-dep-map
| 881 |
Parameter exists_ : forall {A}, (key -> A -> bool) -> forall {dom}, t A dom -> bool.
|
Utf8 Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapFactsInterface
|
coq-contribs-dep-map
| 882 |
Parameter exists_spec : forall A f, Proper (X.eq ==> Logic.eq ==> Logic.eq) f -> forall dom (m : t A dom), exists_ f m = true <-> exists x v, find x m = Some v ∧ f x v = true.
|
Utf8 Orders Coqlib DepMapInterface
|
coq-contribs-dep-map/DepMapFactsInterface
|
coq-contribs-dep-map
| 883 |
Definition eq {A : Type} dom₁ dom₂ (m₁ : t A dom₁) (m₂ : t A dom₂) := forall x, find x m₁ = find x m₂.
|
Utf8 Bool SetoidList RelationPairs Orders Coqlib DepMapInterface DepMapFactsInterface
|
coq-contribs-dep-map/DepMapFactsImplementation
|
coq-contribs-dep-map
| 884 |
Definition incl {A : Type} dom₁ dom₂ (m₁ : t A dom₁) (m₂ : t A dom₂) := forall x v, find x m₁ = Some v -> find x m₂ = Some v.
|
Utf8 Bool SetoidList RelationPairs Orders Coqlib DepMapInterface DepMapFactsInterface
|
coq-contribs-dep-map/DepMapFactsImplementation
|
coq-contribs-dep-map
| 885 |
Definition for_all {A : Type} (f : key -> A -> bool) dom (m : t A dom) := fold (fun x v b => b && f x v) m true.
|
Utf8 Bool SetoidList RelationPairs Orders Coqlib DepMapInterface DepMapFactsInterface
|
coq-contribs-dep-map/DepMapFactsImplementation
|
coq-contribs-dep-map
| 886 |
Definition exists_ {A : Type} (f : key -> A -> bool) dom (m : t A dom) := fold (fun x v b => b || f x v) m false.
|
Utf8 Bool SetoidList RelationPairs Orders Coqlib DepMapInterface DepMapFactsInterface
|
coq-contribs-dep-map/DepMapFactsImplementation
|
coq-contribs-dep-map
| 887 |
Definition OpenTerm0 a := OpenTerm (ne_list.one a).
|
Coq.Classes.RelationClasses Coq.Relations.Relation_Definitions Coq.Lists.List Coq.Classes.Morphisms MathClasses.interfaces.universal_algebra MathClasses.interfaces.abstract_algebra MathClasses.interfaces.canonical_names MathClasses.theory.categories MathClasses.categories.varieties
|
coq-community-math-classes/varieties/open_terms
|
coq-community-math-classes
| 888 |
Fixpoint app_tree {o}: OpenTerm o → op_type OpenTerm0 o := match o with | ne_list.one _ => id | ne_list.cons _ _ => λ x y, app_tree (App _ _ _ _ x y) end.
|
Coq.Classes.RelationClasses Coq.Relations.Relation_Definitions Coq.Lists.List Coq.Classes.Morphisms MathClasses.interfaces.universal_algebra MathClasses.interfaces.abstract_algebra MathClasses.interfaces.canonical_names MathClasses.theory.categories MathClasses.categories.varieties
|
coq-community-math-classes/varieties/open_terms
|
coq-community-math-classes
| 889 |
Definition the_object: varieties.Object et := varieties.object et OpenTerm0.
|
Coq.Classes.RelationClasses Coq.Relations.Relation_Definitions Coq.Lists.List Coq.Classes.Morphisms MathClasses.interfaces.universal_algebra MathClasses.interfaces.abstract_algebra MathClasses.interfaces.canonical_names MathClasses.theory.categories MathClasses.categories.varieties
|
coq-community-math-classes/varieties/open_terms
|
coq-community-math-classes
| 890 |
Definition sig: Signature := single_sorted_signature (λ o, match o with mult => 2%nat end).
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.universal_algebra MathClasses.theory.ua_homomorphisms MathClasses.misc.workaround_tactics categories.categories
|
coq-community-math-classes/varieties/semigroups
|
coq-community-math-classes
| 891 |
Definition theory: EquationalTheory := Build_EquationalTheory sig Laws.
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.universal_algebra MathClasses.theory.ua_homomorphisms MathClasses.misc.workaround_tactics categories.categories
|
coq-community-math-classes/varieties/semigroups
|
coq-community-math-classes
| 892 |
Definition Object := varieties.Object theory.
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.universal_algebra MathClasses.theory.ua_homomorphisms MathClasses.misc.workaround_tactics categories.categories
|
coq-community-math-classes/varieties/semigroups
|
coq-community-math-classes
| 893 |
Definition forget: Object → setoids.Object := @product.project unit (λ _, setoids.Object) (λ _, _: Arrows setoids.Object) _ (λ _, _: CatId setoids.Object) (λ _, _: CatComp setoids.Object) (λ _, _: Category setoids.Object) tt ∘ forget_algebra.object theory ∘ forget_variety.forget theory.
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.universal_algebra MathClasses.theory.ua_homomorphisms MathClasses.misc.workaround_tactics categories.categories
|
coq-community-math-classes/varieties/semigroups
|
coq-community-math-classes
| 894 |
Definition object: Object := varieties.object theory (λ _, A).
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.universal_algebra MathClasses.theory.ua_homomorphisms MathClasses.misc.workaround_tactics categories.categories
|
coq-community-math-classes/varieties/semigroups
|
coq-community-math-classes
| 895 |
Definition op := False.
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.universal_algebra MathClasses.theory.ua_homomorphisms
|
coq-community-math-classes/varieties/setoids
|
coq-community-math-classes
| 896 |
Definition sig: Signature := Build_Signature unit op (False_rect _).
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.universal_algebra MathClasses.theory.ua_homomorphisms
|
coq-community-math-classes/varieties/setoids
|
coq-community-math-classes
| 897 |
Definition Laws: EqEntailment sig → Prop := λ _, False.
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.universal_algebra MathClasses.theory.ua_homomorphisms
|
coq-community-math-classes/varieties/setoids
|
coq-community-math-classes
| 898 |
Definition object: varieties.Object theory := varieties.object theory (λ _, A).
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.universal_algebra MathClasses.theory.ua_homomorphisms
|
coq-community-math-classes/varieties/setoids
|
coq-community-math-classes
| 900 |
Definition sig: Signature := single_sorted_signature (λ o, match o with one => O | mult => 2%nat end).
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.universal_algebra MathClasses.theory.ua_homomorphisms MathClasses.misc.workaround_tactics MathClasses.categories.categories
|
coq-community-math-classes/varieties/monoids
|
coq-community-math-classes
| 901 |
Definition forget: Object → setoids.Object := @product.project unit (λ _, setoids.Object) (λ _, _) _ (λ _, _) (λ _, _) (λ _, _) tt ∘ forget_algebra.object theory ∘ forget_variety.forget theory.
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.universal_algebra MathClasses.theory.ua_homomorphisms MathClasses.misc.workaround_tactics MathClasses.categories.categories
|
coq-community-math-classes/varieties/monoids
|
coq-community-math-classes
| 904 |
Variable et: EquationalTheory.
|
Coq.Classes.RelationClasses Coq.Relations.Relation_Definitions Coq.Lists.List Coq.Classes.Morphisms MathClasses.interfaces.universal_algebra MathClasses.theory.ua_homomorphisms MathClasses.interfaces.abstract_algebra MathClasses.interfaces.canonical_names MathClasses.theory.categories MathClasses.categories.varieties
|
coq-community-math-classes/varieties/closed_terms
|
coq-community-math-classes
| 906 |
Fixpoint app_tree {o}: ClosedTerm o → op_type ClosedTerm0 o := match o with | ne_list.one _ => id | ne_list.cons _ _ => λ x y, app_tree (App _ _ _ _ x y) end.
|
Coq.Classes.RelationClasses Coq.Relations.Relation_Definitions Coq.Lists.List Coq.Classes.Morphisms MathClasses.interfaces.universal_algebra MathClasses.theory.ua_homomorphisms MathClasses.interfaces.abstract_algebra MathClasses.interfaces.canonical_names MathClasses.theory.categories MathClasses.categories.varieties
|
coq-community-math-classes/varieties/closed_terms
|
coq-community-math-classes
| 907 |
Definition the_object: varieties.Object et := varieties.object et ClosedTerm0.
|
Coq.Classes.RelationClasses Coq.Relations.Relation_Definitions Coq.Lists.List Coq.Classes.Morphisms MathClasses.interfaces.universal_algebra MathClasses.theory.ua_homomorphisms MathClasses.interfaces.abstract_algebra MathClasses.interfaces.canonical_names MathClasses.theory.categories MathClasses.categories.varieties
|
coq-community-math-classes/varieties/closed_terms
|
coq-community-math-classes
| 908 |
Variable other: varieties.Object et.
|
Coq.Classes.RelationClasses Coq.Relations.Relation_Definitions Coq.Lists.List Coq.Classes.Morphisms MathClasses.interfaces.universal_algebra MathClasses.theory.ua_homomorphisms MathClasses.interfaces.abstract_algebra MathClasses.interfaces.canonical_names MathClasses.theory.categories MathClasses.categories.varieties
|
coq-community-math-classes/varieties/closed_terms
|
coq-community-math-classes
| 909 |
Definition eval_in_other {o}: ClosedTerm o → op_type other o := @eval et other _ False o (no_vars _ other).
|
Coq.Classes.RelationClasses Coq.Relations.Relation_Definitions Coq.Lists.List Coq.Classes.Morphisms MathClasses.interfaces.universal_algebra MathClasses.theory.ua_homomorphisms MathClasses.interfaces.abstract_algebra MathClasses.interfaces.canonical_names MathClasses.theory.categories MathClasses.categories.varieties
|
coq-community-math-classes/varieties/closed_terms
|
coq-community-math-classes
| 910 |
Definition morph a: the_object a → other a := eval_in_other.
|
Coq.Classes.RelationClasses Coq.Relations.Relation_Definitions Coq.Lists.List Coq.Classes.Morphisms MathClasses.interfaces.universal_algebra MathClasses.theory.ua_homomorphisms MathClasses.interfaces.abstract_algebra MathClasses.interfaces.canonical_names MathClasses.theory.categories MathClasses.categories.varieties
|
coq-community-math-classes/varieties/closed_terms
|
coq-community-math-classes
| 911 |
Definition sig: Signature := single_sorted_signature (λ o, match o with zero | one => O | negate => 1%nat | plus | mult => 2%nat end).
|
Coq.setoid_ring.Ring MathClasses.interfaces.abstract_algebra MathClasses.interfaces.universal_algebra MathClasses.theory.ua_homomorphisms MathClasses.misc.workaround_tactics
|
coq-community-math-classes/varieties/rings
|
coq-community-math-classes
| 912 |
Definition sig: Signature := single_sorted_signature (λ o, match o with one => O | inv => 1%nat | mult => 2%nat end).
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.universal_algebra MathClasses.theory.ua_homomorphisms MathClasses.misc.workaround_tactics categories.categories
|
coq-community-math-classes/varieties/abgroup
|
coq-community-math-classes
| 916 |
Definition sig: Signature := single_sorted_signature (λ o, match o with zero | one => O | plus | mult => 2%nat end).
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.universal_algebra MathClasses.theory.ua_homomorphisms MathClasses.misc.workaround_tactics
|
coq-community-math-classes/varieties/semirings
|
coq-community-math-classes
| 925 |
Definition sig: Signature := Build_Signature False False (False_rect _).
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.universal_algebra
|
coq-community-math-classes/varieties/empty
|
coq-community-math-classes
| 930 |
Definition Laws (_: EqEntailment sig): Prop := False.
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.universal_algebra
|
coq-community-math-classes/varieties/empty
|
coq-community-math-classes
| 931 |
Definition object: Object := varieties.object theory carriers.
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.universal_algebra
|
coq-community-math-classes/varieties/empty
|
coq-community-math-classes
| 934 |
Definition in_domain: Equiv A := λ x y, f x = f y.
|
Coq.Classes.Morphisms Coq.Classes.RelationClasses Coq.Relations.Relation_Definitions Coq.Lists.List MathClasses.interfaces.abstract_algebra MathClasses.interfaces.universal_algebra MathClasses.theory.ua_homomorphisms MathClasses.interfaces.canonical_names MathClasses.theory.ua_subalgebraT MathClasses.misc.util
|
coq-community-math-classes/theory/ua_congruence
|
coq-community-math-classes
| 935 |
Definition image s (b: B s): Type := sigT (λ a, f s a = b).
|
Coq.Classes.Morphisms Coq.Classes.RelationClasses Coq.Relations.Relation_Definitions Coq.Lists.List MathClasses.interfaces.abstract_algebra MathClasses.interfaces.universal_algebra MathClasses.theory.ua_homomorphisms MathClasses.interfaces.canonical_names MathClasses.theory.ua_subalgebraT MathClasses.misc.util
|
coq-community-math-classes/theory/ua_congruence
|
coq-community-math-classes
| 936 |
Definition quot_obj: algebras.Object σ := algebras.object σ A (algebra_equiv:=Φ).
|
Coq.Classes.Morphisms Coq.Classes.RelationClasses Coq.Relations.Relation_Definitions Coq.Lists.List MathClasses.interfaces.abstract_algebra MathClasses.interfaces.universal_algebra MathClasses.theory.ua_homomorphisms MathClasses.interfaces.canonical_names MathClasses.theory.ua_subalgebraT MathClasses.misc.util
|
coq-community-math-classes/theory/ua_congruence
|
coq-community-math-classes
| 937 |
Definition subobject: algebras.Object σ := algebras.object σ (ua_subalgebraT.carrier image).
|
Coq.Classes.Morphisms Coq.Classes.RelationClasses Coq.Relations.Relation_Definitions Coq.Lists.List MathClasses.interfaces.abstract_algebra MathClasses.interfaces.universal_algebra MathClasses.theory.ua_homomorphisms MathClasses.interfaces.canonical_names MathClasses.theory.ua_subalgebraT MathClasses.misc.util
|
coq-community-math-classes/theory/ua_congruence
|
coq-community-math-classes
| 938 |
Variable Sorts: Set.
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.universal_algebra
|
coq-community-math-classes/theory/ua_mapped_operations
|
coq-community-math-classes
| 939 |
Fixpoint map_op {o: OpType Sorts}: op_type A o → op_type B o := match o return op_type A o → op_type B o with | ne_list.one u => ab u | ne_list.cons _ _ => λ x y, map_op (x (ba _ y)) end.
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.universal_algebra
|
coq-community-math-classes/theory/ua_mapped_operations
|
coq-community-math-classes
| 940 |
Definition Pvars (vars: Vars et (carrier P) nat): Vars et A nat := λ s n, ` (vars s n).
|
Coq.Classes.RelationClasses Coq.Classes.Morphisms Coq.Program.Program MathClasses.interfaces.abstract_algebra MathClasses.interfaces.universal_algebra MathClasses.interfaces.canonical_names MathClasses.theory.ua_subalgebra
|
coq-community-math-classes/theory/ua_subvariety
|
coq-community-math-classes
| 941 |
Definition homFrom (y: C): setoids.Object := setoids.object (x ⟶ y).
|
MathClasses.interfaces.abstract_algebra MathClasses.theory.setoids MathClasses.interfaces.functors MathClasses.theory.categories
|
coq-community-math-classes/theory/hom_functor
|
coq-community-math-classes
| 942 |
Definition rationals_to_rationals Q1 Q2 `{Rationals Q1} `{Rationals Q2} : Q1 → Q2 := (rationals_to_frac Q2 (SRpair nat))⁻¹ ∘ rationals_to_frac Q1 (SRpair nat).
|
Coq.setoid_ring.Ring MathClasses.interfaces.abstract_algebra MathClasses.interfaces.integers MathClasses.interfaces.naturals MathClasses.interfaces.rationals MathClasses.implementations.field_of_fractions MathClasses.implementations.natpair_integers MathClasses.theory.rings MathClasses.theory.integers MathClasses.theory.dec_fields
|
coq-community-math-classes/theory/rationals
|
coq-community-math-classes
| 943 |
Fixpoint op_closed {o: OpType (sorts sign)}: op_type A o → Prop := match o with | ne_list.one x => P x | ne_list.cons _ _ => λ d, ∀ z, P _ z → op_closed (d z) end.
|
Coq.Classes.RelationClasses MathClasses.interfaces.universal_algebra MathClasses.theory.ua_homomorphisms MathClasses.interfaces.canonical_names MathClasses.theory.categories MathClasses.interfaces.abstract_algebra
|
coq-community-math-classes/theory/ua_subalgebra
|
coq-community-math-classes
| 944 |
Definition carrier s := sig (P s).
|
Coq.Classes.RelationClasses MathClasses.interfaces.universal_algebra MathClasses.theory.ua_homomorphisms MathClasses.interfaces.canonical_names MathClasses.theory.categories MathClasses.interfaces.abstract_algebra
|
coq-community-math-classes/theory/ua_subalgebra
|
coq-community-math-classes
| 945 |
Definition close_op_proper d (o0 o1: op_type A d) (P': op_closed o0) (Q: op_closed o1): o0 = o1 → close_op o0 P' = close_op o1 Q.
|
Coq.Classes.RelationClasses MathClasses.interfaces.universal_algebra MathClasses.theory.ua_homomorphisms MathClasses.interfaces.canonical_names MathClasses.theory.categories MathClasses.interfaces.abstract_algebra
|
coq-community-math-classes/theory/ua_subalgebra
|
coq-community-math-classes
| 946 |
Definition proj s := @proj1_sig (A s) (P s).
|
Coq.Classes.RelationClasses MathClasses.interfaces.universal_algebra MathClasses.theory.ua_homomorphisms MathClasses.interfaces.canonical_names MathClasses.theory.categories MathClasses.interfaces.abstract_algebra
|
coq-community-math-classes/theory/ua_subalgebra
|
coq-community-math-classes
| 947 |
Definition forget (v: varieties.Object et) := algebras.object et v.
|
MathClasses.interfaces.canonical_names MathClasses.interfaces.abstract_algebra MathClasses.interfaces.universal_algebra MathClasses.interfaces.functors MathClasses.theory.categories MathClasses.categories.varieties MathClasses.categories.algebras
|
coq-community-math-classes/theory/forget_variety
|
coq-community-math-classes
| 949 |
Definition prod_equiv `{Equiv A} `{Equiv B} : Equiv (A * B) := λ p q, fst p = fst q ∧ snd p = snd q.
|
MathClasses.interfaces.abstract_algebra
|
coq-community-math-classes/theory/products
|
coq-community-math-classes
| 950 |
Definition prod_fst_equiv X A `{Equiv X} : relation (X * A) := λ x y, fst x = fst y.
|
MathClasses.interfaces.abstract_algebra
|
coq-community-math-classes/theory/products
|
coq-community-math-classes
| 951 |
Definition fset_car_setoid A `{FSet A} : Setoid A := setoidmor_a singleton.
|
MathClasses.theory.lattices MathClasses.varieties.monoids MathClasses.implementations.bool MathClasses.implementations.list_finite_set MathClasses.orders.lattices MathClasses.interfaces.abstract_algebra MathClasses.interfaces.finite_sets MathClasses.interfaces.orders
|
coq-community-math-classes/theory/finite_sets
|
coq-community-math-classes
| 952 |
Variable σ: Signature.
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.universal_algebra
|
coq-community-math-classes/theory/ua_homomorphisms
|
coq-community-math-classes
| 953 |
Fixpoint Preservation {n : OpType}: op_type A n → op_type B n → Prop := match n with | ne_list.one d => λ oA oB, f oA = oB | ne_list.cons x y => λ oA oB, ∀ x, Preservation (oA x) (oB (f x)) end.
|
MathClasses.interfaces.abstract_algebra MathClasses.interfaces.universal_algebra
|
coq-community-math-classes/theory/ua_homomorphisms
|
coq-community-math-classes
| 954 |
CoInductive Stream_eq_coind (s1 s2: ∞A) : Prop := stream_eq_coind : hd s1 = hd s2 → Stream_eq_coind (tl s1) (tl s2) → Stream_eq_coind s1 s2.
|
MathClasses.theory.CoqStreams MathClasses.implementations.peano_naturals MathClasses.interfaces.abstract_algebra
|
coq-community-math-classes/theory/streams
|
coq-community-math-classes
| 955 |
Definition EventuallyForAll (P : ∞A → Prop) := ForAll (λ s, P s → P (tl s)).
|
MathClasses.theory.CoqStreams MathClasses.implementations.peano_naturals MathClasses.interfaces.abstract_algebra
|
coq-community-math-classes/theory/streams
|
coq-community-math-classes
| 956 |
CoFixpoint iterate (f:A → A) (x:A) : ∞A := x ::: iterate f (f x).
|
MathClasses.theory.CoqStreams MathClasses.implementations.peano_naturals MathClasses.interfaces.abstract_algebra
|
coq-community-math-classes/theory/streams
|
coq-community-math-classes
| 957 |
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