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