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


DEBUG:Going to execute:
intros