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 : ∀ x : A, nth_error (a :: l) 0 = Some x → g (f n x) = g' (f' n x)
  ============================
   (nth_error (a :: l) 0 = Some a)


DEBUG:Going to execute:
let rec use_hyps :=
            match goal with
            | H:_ ∧ _ |- _ => exact H || (destruct_hyp H; use_hyps)
            | H:_ * _ |- _ => exact H || (destruct_hyp H; use_hyps)
            | H:_ |- _ => solve [ inversion H ]
            | _ => idtac
            end
           in
           let do_atom := solve
           [ trivial
           with eq_true
           | reflexivity
           | symmetry; trivial
           | contradiction
           | congruence ]
           in
           let rec do_ccl :=
            try do_atom; repeat (do_intro; try do_atom); try arith_congr;
             (solve [ split; do_ccl ])
           in
           (solve [ do_atom | use_hyps; do_ccl ]) ||
             fail "Cannot solve this goal"