90bfd84a07
In the standard library, we should use explicit universe variables for universe polymorphic definitions. Users that want to declare universe polymorphic definitions but do not want to provide universe level parameters should use Type _ or Type*
38 lines
1.1 KiB
Text
38 lines
1.1 KiB
Text
section
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variable {A : Type*}
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variable f : A → A → A
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variable one : A
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variable inv : A → A
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local infixl `*` := f
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local postfix `^-1`:100 := inv
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definition is_assoc := ∀ a b c, (a*b)*c = a*b*c
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definition is_id := ∀ a, a*one = a
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definition is_inv := ∀ a, a*a^-1 = one
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end
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inductive [class] group_struct (A : Type*) : Type*
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| mk_group_struct : Π (mul : A → A → A) (one : A) (inv : A → A), is_assoc mul → is_id mul one → is_inv mul one inv → group_struct
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inductive group : Type*
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| mk_group : Π (A : Type*), group_struct A → group
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definition carrier (g : group) : Type*
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:= group.rec (λ c s, c) g
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attribute [instance]
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definition group_to_struct (g : group) : group_struct (carrier g)
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:= group.rec (λ (A : Type*) (s : group_struct A), s) g
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check group_struct
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definition mul1 {A : Type*} {s : group_struct A} (a b : A) : A
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:= group_struct.rec (λ mul one inv h1 h2 h3, mul) s a b
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infixl `*` := mul1
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constant G1 : group.{1}
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constant G2 : group.{1}
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constants a b c : (carrier G2)
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constants d e : (carrier G1)
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check a * b * b
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check d * e
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