Goal:
  
  A : Type
  B : Type
  P : A → B → Type
  Q : A → B → Type
  a : A
  l : list A
  IHl : ∀ l' : list B,
          All2 P l l'
          → (∀ (x : A) (y : B), In x l → In y l' → P x y → Q x y)
            → All2 Q l l'
  y : B
  l'0 : list B
  X0 : ∀ (x : A) (y0 : B), In x (a :: l) → In y0 (y :: l'0) → P x y0 → Q x y0
  X : All2 P (a :: l) (y :: l'0)
  X1 : P a y
  X2 : All2 P l l'0
  x : A
  y0 : B
  H : In x l
  H0 : In y0 l'0
  X3 : P x y0
  ============================
   (In y0 l'0)


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"