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


DEBUG:Going to execute:
match goal with
           | |- well_founded _ => auto with *
           | |- ?T => match type of T with
                      | Prop => auto
                      end
           end