let
  sym : (A : Type) (x y : A) -> Path (\x -> A) x y -> Path (\x -> A) y x
    = λ A x y p i -> p (~ i)
in let
  funext : (A : Type) (B : A -> Type) (f g : (x : A) -> B x) -> ((x : A) -> Path (\i -> B x) (f x) (g x)) -> Path (\i -> (x : A) -> B x) f g
    = λ A B f g h i x -> h x i
in let
  i0IsI1 : Path (\x -> I) i0 i1
    = λ i -> i
in let
  singContr : (A : Type) (a b : A) (p : Path (\j -> A) a b) -> Path (\i -> (x : A) * (Path (\j -> A) a x)) (a, \i -> a) (b, p)
    = λ A a b p i -> (p i, λ j -> p (i && j))
in let
  transport : (A : I -> Type) (a : A i0) -> A i1
    = \A a -> comp A i0 (\i -> []) a
in let
  Jay : (A : Type) (x : A)
        (P : (y : A) -> Path (\i -> A) x y -> Type)
        (d : P x (\i -> x))
        (y : A) (p : Path (\i -> A) x y)
     -> P y p
    = \A x P d y p -> transport (\i -> P (p i) (\j -> p (i && j))) d
in Jay