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


DEBUG:Going to execute:
trivial; hnf; intros; (solve
            [ do
            ![ solve
             [ trivial | apply : eq_sym ; trivial ]
             | discriminate
             | contradiction
             | Ltac.split ]
            | case not_locked_false_eq_true; Ltac.assumption
            | match goal with
              | H:¬ _ |- _ => solve [ case H; trivial ]
              end ])