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