module Quox.OPE.Length

import Quox.OPE.Basics

%default total


public export
data Length : Scope a -> Type where
  Z : Length [<]
  S : (s : Length xs) -> Length (xs :< x)
%name Length s
%builtin Natural Length

public export
(.nat) : Length xs -> Nat
(Z).nat   = Z
(S s).nat = S s.nat
%transform "Length.nat" Length.(.nat) xs = believe_me xs

export
0 ok : (s : Length xs) -> s.nat = length xs
ok Z     = Refl
ok (S s) = cong S $ ok s