lean2/tests/lean/run/impbug3.lean
2014-09-19 15:54:32 -07:00

22 lines
600 B
Text

-- category
definition Prop := Type.{0}
variable eq {A : Type} : A → A → Prop
infix `=`:50 := eq
variable ob : Type.{1}
variable mor : ob → ob → Type.{1}
inductive category : Type :=
mk : Π (id : Π (A : ob), mor A A),
(Π (A B : ob) (f : mor A A), id A = f) → category
definition id (Cat : category) := category.rec (λ id idl, id) Cat
variable Cat : category
theorem id_left (A : ob) (f : mor A A) : @eq (mor A A) (id Cat A) f :=
@category.rec (λ (C : category), @eq (mor A A) (id C A) f)
(λ (id : Π (T : ob), mor T T)
(idl : Π (T : ob), _),
idl A A f)
Cat