Goal:
  
  A : Type
  x : A
  xs : list A
  f : A → bool
  H0 : ∀ f0 : A → bool,
         (λ (x : A) (_ : In x xs), f x) = (λ (x : A) (_ : In x xs), f0 x)
         → forallb_InP xs (λ (x : A) (_ : In x xs), f x) = forallb f0 xs
  ============================
   (forallb_InP (x :: xs) (λ (x0 : A) (_ : In x0 (x :: xs)), f x0) =
    forallb f (x :: xs))


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 ])