24 lines
634 B
Text
24 lines
634 B
Text
prelude
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-- category
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definition Prop := Type.{0}
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constant eq {A : Type} : A → A → Prop
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infix `=`:50 := eq
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constant ob : Type.{1}
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constant mor : ob → ob → Type.{1}
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inductive category : Type
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| mk : Π (id : Π (A : ob), mor A A),
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(Π (A B : ob) (f : mor A A), id A = f) → category
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definition id (Cat : category) := category.rec (λ id idl, id) Cat
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constant Cat : category
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attribute id [reducible]
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theorem id_left (A : ob) (f : mor A A) : @eq (mor A A) (id Cat A) f :=
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@category.rec (λ (C : category), @eq (mor A A) (id C A) f)
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(λ (id : Π (T : ob), mor T T)
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(idl : Π (T : ob), _),
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idl A A f)
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Cat
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