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
  H : p a
      ∧ (fix forallb (l : list A) : bool :=
           match l with
           | [] => true
           | a :: l0 => p a && forallb l0
           end) l
  ============================
   (is_true (forallb p l))


DEBUG:Going to execute:
fun H => case H; clear H; do_intro; do_intro