Goal:
  
  A : Type
  B : Type
  P : list A → list A → A → A → B → Type
  a : B
  ls1 : list B
  IH : ∀ ls2 ls3 : list A,
         All
           (λ z : B,
              All2_fold (λ (l1 l2 : list A) (x y : A), P l1 l2 x y z) ls2 ls3)
           ls1
         → (ls1 = []) +
           All2_fold (λ (l1 l2 : list A) (x y : A), All (P l1 l2 x y) ls1)
             ls2 ls3
  a0 : A
  ls3 : list A
  X : All
        (λ z : B,
           All2_fold (λ (l1 l2 : list A) (x y : A), P l1 l2 x y z) []
             (a0 :: ls3)) (a :: ls1)
  ============================
   ((a :: ls1 = []) +
    All2_fold (λ (l1 l2 : list A) (x y : A), All (P l1 l2 x y) (a :: ls1)) []
      (a0 :: ls3))%type


DEBUG:Going to execute:
first
[ All2_All_swap_t_step
| let H1 := fresh in
  let H2 := fresh in
  eapply All2_fold_impl;
   [ eapply All2_fold_prod
   | intros * [H1 H2]; constructor; (first [ exact H1 | exact H2 ]) ];
   (let IH' := fresh in
    eauto; edestruct IH as [IH'| IH']; try (apply IH'; clear IH'); clear IH) ]