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 ∥ -> ∥ Alli P (S k) l ∥ -> ∥ Alli P k (a :: l) ∥)


DEBUG:Going to execute:
<coq-equations.plugin::simplify@0> $1