Goal:
  
  A : Type
  p : A → bool
  a : A
  l : list A
  n : nat
  x : A
  Hnth : nth_error (a :: l) (S n) = Some x
  IHl : ∀ n : nat, nth_error l n = Some x → forallb p l → p x
  ============================
   (p a
    ∧ (fix forallb (l : list A) : bool :=
         match l with
         | [] => true
         | a :: l0 => p a && forallb l0
         end) l → forallb p l)


DEBUG:Going to execute:
try do_atom; repeat (do_intro; try do_atom); try arith_congr