2014-12-01 05:16:01 +00:00
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prelude
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2014-09-09 16:25:35 +00:00
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-- category
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2014-09-17 21:39:05 +00:00
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definition Prop := Type.{0}
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2014-10-02 23:20:52 +00:00
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constant eq {A : Type} : A → A → Prop
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2014-09-09 16:25:35 +00:00
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infix `=`:50 := eq
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2014-10-02 23:20:52 +00:00
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constant ob : Type.{1}
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constant mor : ob → ob → Type.{1}
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2014-09-09 16:25:35 +00:00
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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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2014-09-17 21:39:05 +00:00
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definition id (Cat : category) := category.rec (λ id idl, id) Cat
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2014-10-02 23:20:52 +00:00
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constant Cat : category
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2014-09-09 16:25:35 +00:00
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print "-----------------"
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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
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(λ (C : category), Π (A B : ob) (f : mor A A), @eq (mor A A) (id C A) f)
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(λ id idl, idl)
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Cat A A f
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