Goal:
  
  T : Type -> Type
  M : Monad T
  A : Type
  P : nat -> A -> Type
  l0 : list A
  k : nat
  f : forall (n : nat) (x : A),
      nth_error l0 n = Some x -> T (∥ P (k + n) x ∥)
  a : A
  l : list A
  Heq_l : a :: l = l0
  X : ∥ P (k + 0) a ∥
  n : nat
  x : A
  hnth : nth_error l n = Some x
  ============================
   (nth_error l n = match l0 with
                    | [] => None
                    | _ :: l => nth_error l n
                    end)


DEBUG:Going to execute:
repeat (Tactics.destruct_conjs; simpl proj1_sig in *)