type0 : Type
typeof(type0) : Type(1)
type tower: [Type;Type(1);Type(2);Type(3);Type(4)]
a: a, b: b, typeof(a): Bool
b2b: (Bool -> Bool)
p(a): p a
p(b): p b
q(a): q a
q(b): q b
typeof(p a): Bool
lxy_px: (\x:Bool. (\y:Bool. p x[1]))
  type: (Bool -> (Bool -> Bool))
  type of type: Type
lxy_px a b: ((\x:Bool. (\y:Bool. p x[1]))) a b
  type: Bool
(=): =
  type: (Pi Alpha:Type. (Pi _:Alpha[0]. (Alpha[1] -> Bool)))
p2: p2
  type: (tau -> (tau -> Bool))
t2: = ((tau -> (tau -> Bool))) ((\x:tau. (\y:tau. p2 x[1] y[0]))) (= tau)
  type: Bool