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
  ls2 : list A
  a1 : A
  ls3 : list A
  X1 : All
         (λ z : B,
            All2_fold (λ (l1 l2 : list A) (x y : A), P l1 l2 x y z)
              (a0 :: ls2) (a1 :: ls3)) ls1
  X : All2_fold (λ (l1 l2 : list A) (x y : A), P l1 l2 x y a) ls2 ls3
  X2 : P ls2 ls3 a0 a1 a
  ============================
   (All2_fold (λ (l1 l2 : list A) (x y : A), All (P l1 l2 x y) (a :: ls1))
      ls2 ls3)


DEBUG:Going to execute:
(first
            [ eapply All2_impl | eapply All2_fold_impl | eapply All_impl ]);
            tea; cbn; intros *; inversion 1 + constructor; subst; eauto
Level 0: Backtrace:

Proof is not complete.
Level 0: Backtrace:

Proof is not complete.