Goal:
    T : Type -> Type  M : 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:
<coq-equations.plugin::simplify@0> $1