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 : is_true (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:
do_intro
Level 4: Backtrace:

Proof is not complete.
Level 4: Backtrace:

No applicable tactic.
Level 3: evaluation returns
idtac of type tacvalue