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


DEBUG:Going to execute:
intro || (let H := fresh in
                     intro
                     H)
DEBUG LTAC Evaluated term: (forall (A : Type) (P : nat -> A -> Type)
                              (k : nat) (a : A) (l : list A),
                            (forall (n : nat) (x : A),
                             nth_error (a :: l) n = Some x ->
                             T (∥ P (k + n) x ∥)) ->
                            ∥ P (k + 0) a ∥ ->
                            ∥ Alli P (S k) l ∥ -> ∥ Alli P k (a :: l) ∥)
DEBUG LTAC Evaluated term: Prop