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 ∥)
  Y : Alli P (S k) l
  X : P (k + 0) a
  ============================
   (∥ Alli P k (a :: l) ∥)


DEBUG:Going to execute:
match goal with
           | H:∥ _ ∥ |- _ => case H; clear H; intro H
           end