Goal:
  
  A : Type
  B : Type
  f : nat → A → B
  f' : nat → A → B
  g : B → bool
  g' : B → bool
  a : A
  l : list A
  IHl : ∀ n : nat,
          (∀ (n0 : nat) (x : A),
             nth_error l n0 = Some x → g (f (n + n0) x) → g' (f' (n + n0) x))
          → forallb g (mapi_rec f l n) → forallb g' (mapi_rec f' l n)
  n : nat
  hfg : ∀ (n0 : nat) (x : A),
          nth_error (a :: l) n0 = Some x
          → g (f (n + n0) x) → g' (f' (n + n0) x)
  hg : is_true (g' (f' n a))
  hf : is_true (forallb g (mapi_rec f l (S n)))
  H : ∀ x : A, nth_error (a :: l) 0 = Some x → g (f n x) → g' (f' n x)
  ============================
   (is_true (g' (f' n a) && forallb g' (mapi_rec f' l (S n))))


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 ])