Goal:
  
  A : Type
  B : Type
  P : A → nat → B → Type
  a : B
  ls1 : list B
  a0 : A
  ls2 : list A
  n : nat
  X2 : Alli (P a0) (S n) ls1
  X3 : All (λ x : A, Alli (P x) (S n) ls1) ls2
  X1 : P a0 n a
  X4 : All (λ x : A, P x n a) ls2
  X0 : All (λ x : A, P x n a) (a0 :: ls2)
  X5 : Alli (λ (n : nat) (y : B), All (λ x : A, P x n y) (a0 :: ls2)) 
         (S n) ls1
  ============================
   (All (λ x : A, Alli (P x) n (a :: ls1)) ls2)


DEBUG:Going to execute:
let rec use_hyp H :=
            match type of H with
            | _ ∧ _ => exact H || destruct_hyp H
            | _ * _ => exact H || destruct_hyp H
            | _ => try (solve [ inversion H ])
            end
           with do_intro := let H := fresh in
                            intro H; use_hyp H
           with destruct_hyp H := case H; clear H; do_intro; do_intro
           in
           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"