lean2/tests/lean/run/impbug1.lean

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