Goal:
  
  T : Type -> Type
  M : Monad T
  A : Type
  P : nat -> A -> Type
  k : nat
  a : A
  ============================
   (forall l : list A,
    (forall (n : nat) (x : A),
     nth_error (a :: l) n = Some x -> T (∥ P (k + n) x ∥)) ->
    ∥ P (k + 0) a ∥ ->
    forall (n : nat) (x : A),
    nth_error l n = Some x -> nth_error l n = nth_error l n)


DEBUG:Going to execute:
simplify *