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:
easy
DEBUG LTAC Evaluated term: HPl
DEBUG LTAC Evaluated term: andb_and
DEBUG LTAC Evaluated term: (iffLR
                              (Q:=p a
                                  ∧ (fix forallb (l : list A) : bool :=
                                       match l with
                                       | [] => true
                                       | a :: l0 => p a && forallb l0
                                       end) l)
                              (andb_and (p a)
                                 ((fix forallb (l : list A) : bool :=
                                     match l with
                                     | [] => true
                                     | a :: l0 => p a && forallb l0
                                     end) l)) _view_subject_)