type0 : Type
typeof(type0) : Type(1)
type tower: [Type;Type(1);Type(2);Type(3);Type(4)]
Bool: [true, false]
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 A:Type. (Pi _:A[0]. (A[1] -> Bool)))
p2: p2
  type: (tau -> (tau -> Bool))
t2: (= (tau -> (tau -> Bool)) (\x:tau. (\y:tau. (p2 x[1] y[0]))) (= tau))
  type: Bool
f_vec: vec
  type: (Type -> (nat -> Type))
  type of type: Type(1)