17 lines
898 B
Text
17 lines
898 B
Text
inductive imf {A B : Sort*} (f : A → B) : B → Sort*
|
|
| mk : ∀ (a : A), imf (f a)
|
|
|
|
definition inv_1 {A B : Sort*} (f : A → B) : ∀ (b : B), imf f b → A
|
|
| .(f .(a)) (imf.mk .(f) a) := a -- Error inaccessible annotation inside inaccessible annotation
|
|
|
|
definition inv_2 {A B : Sort*} (f : A → B) : ∀ (b : B), imf f b → A
|
|
| .(f a) (let x := (imf.mk .(f) a) in x) := a -- Error invalid occurrence of 'let' expression
|
|
|
|
definition inv_3 {A B : Sort*} (f : A → B) : ∀ (b : B), imf f b → A
|
|
| .(f a) ((λ (x : imf f b), x) (imf.mk .(f) a)) := a -- Error invalid occurrence of 'lambda' expression
|
|
|
|
definition sym {A : Sort*} : ∀ a b : A, a = b → b = a
|
|
| .(a) .(a) (eq.refl a) := rfl -- Error `a` in eq.refl must be marked as inaccessible since it is an inductive datatype parameter
|
|
|
|
definition symm2 {A : Sort*} : ∀ a b : A, a = b → b = a
|
|
| _ _ rfl := rfl -- correct version
|