Goal:
  
  A : Type
  B : Type
  f : nat → A → bool
  g : nat → B → A
  a : B
  l : list B
  IHl : ∀ n : nat,
          alli f n (mapi_rec g l n) =
          alli (λ (i : nat) (x : B), f i (g i x)) n l
  n : nat
  ============================
   (f n (g n a) && alli (λ (i : nat) (x : B), f i (g i x)) (S n) l =
    f n (g n a) && alli (λ (i : nat) (x : B), f i (g i x)) (S n) l)


DEBUG:Going to execute:
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"