module Equality

-- we don't have implicits yet, so this won't typecheck

Eq : {A : U} -> A -> A -> U
Eq = \ {A} => \ x => \ y => (P : A -> U) -> P x -> P y

refl : {A : U} {x : A} -> Eq x x
refl = \ {A} => \ {x} => x

-- can I write J without pattern matching?
J : {A : U} {x y : A} (eq : Eq x y) ->
(mot : (x : A) (P : Eq x y) -> U)
(b : mot y refl) -> 
mot x eq