Goal:
  
  A : Type
  p : A → bool
  a : A
  l : list A
  IHl : ∀ n : nat, nth_error l n = Some a → forallb p l → p a
  ============================
   (p a ∧ forallb p l → p a)


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