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
  X : All
        (λ z : B,
           All2_fold (λ (l1 l2 : list A) (x y : A), P l1 l2 x y z)
             (a0 :: ls2) (a1 :: ls3)) (a :: ls1)
  ============================
   ((a :: ls1 = []) +
    All2_fold (λ (l1 l2 : list A) (x y : A), All (P l1 l2 x y) (a :: ls1))
      (a0 :: ls2) (a1 :: ls3))%type


DEBUG:Going to execute:
intros