193 lines
5.5 KiB
Text
193 lines
5.5 KiB
Text
/-
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Copyright (c) 2015 Jeremy Avigad. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Jeremy Avigad
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Bundled structures
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-/
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import algebra.group
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open algebra pointed is_trunc
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namespace algebra
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structure Semigroup :=
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(carrier : Type) (struct : semigroup carrier)
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attribute Semigroup.carrier [coercion]
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attribute Semigroup.struct [instance]
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structure CommSemigroup :=
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(carrier : Type) (struct : comm_semigroup carrier)
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attribute CommSemigroup.carrier [coercion]
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attribute CommSemigroup.struct [instance]
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structure Monoid :=
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(carrier : Type) (struct : monoid carrier)
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attribute Monoid.carrier [coercion]
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attribute Monoid.struct [instance]
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structure CommMonoid :=
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(carrier : Type) (struct : comm_monoid carrier)
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attribute CommMonoid.carrier [coercion]
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attribute CommMonoid.struct [instance]
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structure Group :=
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(carrier : Type) (struct : group carrier)
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attribute Group.carrier [coercion]
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attribute Group.struct [instance]
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section
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local attribute Group.struct [instance]
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definition pSet_of_Group [constructor] [reducible] [coercion] (G : Group) : Set* :=
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ptrunctype.mk G !semigroup.is_set_carrier 1
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end
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attribute algebra._trans_of_pSet_of_Group [unfold 1]
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attribute algebra._trans_of_pSet_of_Group_1 algebra._trans_of_pSet_of_Group_2 [constructor]
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definition pType_of_Group [reducible] [constructor] : Group → Type* :=
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algebra._trans_of_pSet_of_Group_1
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definition Set_of_Group [reducible] [constructor] : Group → Set :=
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algebra._trans_of_pSet_of_Group_2
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definition AddGroup : Type := Group
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definition AddGroup.mk [constructor] [reducible] (G : Type) (H : add_group G) : AddGroup :=
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Group.mk G H
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definition AddGroup.struct [reducible] (G : AddGroup) : add_group G :=
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Group.struct G
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attribute AddGroup.struct Group.struct [instance] [priority 2000]
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structure AbGroup :=
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(carrier : Type) (struct : ab_group carrier)
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attribute AbGroup.carrier [coercion]
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definition AddAbGroup : Type := AbGroup
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definition AddAbGroup.mk [constructor] [reducible] (G : Type) (H : add_ab_group G) :
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AddAbGroup :=
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AbGroup.mk G H
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definition AddAbGroup.struct [reducible] (G : AddAbGroup) : add_ab_group G :=
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AbGroup.struct G
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attribute AddAbGroup.struct AbGroup.struct [instance] [priority 2000]
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definition Group_of_AbGroup [coercion] [constructor] (G : AbGroup) : Group :=
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Group.mk G _
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attribute algebra._trans_of_Group_of_AbGroup_1
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algebra._trans_of_Group_of_AbGroup
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algebra._trans_of_Group_of_AbGroup_3 [constructor]
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attribute algebra._trans_of_Group_of_AbGroup_2 [unfold 1]
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definition ab_group_AbGroup [instance] (G : AbGroup) : ab_group G :=
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AbGroup.struct G
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definition add_ab_group_AddAbGroup [instance] (G : AddAbGroup) : add_ab_group G :=
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AbGroup.struct G
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-- structure AddSemigroup :=
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-- (carrier : Type) (struct : add_semigroup carrier)
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-- attribute AddSemigroup.carrier [coercion]
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-- attribute AddSemigroup.struct [instance]
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-- structure AddCommSemigroup :=
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-- (carrier : Type) (struct : add_comm_semigroup carrier)
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-- attribute AddCommSemigroup.carrier [coercion]
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-- attribute AddCommSemigroup.struct [instance]
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-- structure AddMonoid :=
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-- (carrier : Type) (struct : add_monoid carrier)
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-- attribute AddMonoid.carrier [coercion]
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-- attribute AddMonoid.struct [instance]
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-- structure AddCommMonoid :=
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-- (carrier : Type) (struct : add_comm_monoid carrier)
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-- attribute AddCommMonoid.carrier [coercion]
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-- attribute AddCommMonoid.struct [instance]
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-- structure AddGroup :=
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-- (carrier : Type) (struct : add_group carrier)
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-- attribute AddGroup.carrier [coercion]
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-- attribute AddGroup.struct [instance]
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-- structure AddAbGroup :=
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-- (carrier : Type) (struct : add_ab_group carrier)
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-- attribute AddAbGroup.carrier [coercion]
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-- attribute AddAbGroup.struct [instance]
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-- some bundled infinity-structures
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structure InfGroup :=
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(carrier : Type) (struct : inf_group carrier)
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attribute InfGroup.carrier [coercion]
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attribute InfGroup.struct [instance]
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section
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local attribute InfGroup.struct [instance]
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definition pType_of_InfGroup [constructor] [reducible] [coercion] (G : InfGroup) : Type* :=
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pType.mk G 1
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end
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attribute algebra._trans_of_pType_of_InfGroup [unfold 1]
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definition AddInfGroup : Type := InfGroup
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definition AddInfGroup.mk [constructor] [reducible] (G : Type) (H : add_inf_group G) :
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AddInfGroup :=
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InfGroup.mk G H
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definition AddInfGroup.struct [reducible] (G : AddInfGroup) : add_inf_group G :=
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InfGroup.struct G
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attribute AddInfGroup.struct InfGroup.struct [instance] [priority 2000]
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structure AbInfGroup :=
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(carrier : Type) (struct : ab_inf_group carrier)
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attribute AbInfGroup.carrier [coercion]
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definition AddAbInfGroup : Type := AbInfGroup
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definition AddAbInfGroup.mk [constructor] [reducible] (G : Type) (H : add_ab_inf_group G) :
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AddAbInfGroup :=
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AbInfGroup.mk G H
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definition AddAbInfGroup.struct [reducible] (G : AddAbInfGroup) : add_ab_inf_group G :=
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AbInfGroup.struct G
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attribute AddAbInfGroup.struct AbInfGroup.struct [instance] [priority 2000]
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definition InfGroup_of_AbInfGroup [coercion] [constructor] (G : AbInfGroup) : InfGroup :=
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InfGroup.mk G _
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attribute algebra._trans_of_InfGroup_of_AbInfGroup_1 [constructor]
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attribute algebra._trans_of_InfGroup_of_AbInfGroup [unfold 1]
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definition InfGroup_of_Group [constructor] (G : Group) : InfGroup :=
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InfGroup.mk G _
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definition AddInfGroup_of_AddGroup [constructor] (G : AddGroup) : AddInfGroup :=
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AddInfGroup.mk G _
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definition AbInfGroup_of_AbGroup [constructor] (G : AbGroup) : AbInfGroup :=
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AbInfGroup.mk G _
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definition AddAbInfGroup_of_AddAbGroup [constructor] (G : AddAbGroup) : AddAbInfGroup :=
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AddAbInfGroup.mk G _
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end algebra
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