Goal:
  
  A : Type
  B : Type
  P : list A → list A → A → A → B → Type
  b : B
  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)
           (b :: ls1)
         → All2_fold
             (λ (l1 l2 : list A) (x y : A), All (P l1 l2 x y) (b :: ls1)) ls2
             ls3
  a0 : A
  ls2 : list A
  a1 : A
  ls3 : list A
  X : All2_fold (λ (l1 l2 : list A) (x y : A), P l1 l2 x y b) ls2 ls3
  X2 : P ls2 ls3 a0 a1 b
  X3 : 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
  X1 : All2_fold (λ (l1 l2 : list A) (x y : A), P l1 l2 x y a) ls2 ls3
  X4 : P ls2 ls3 a0 a1 a
  ============================
   (All2_fold
      (λ (l1 l2 : list A) (x y : A), All (P l1 l2 x y) (b :: a :: ls1))
      (a0 :: ls2) (a1 :: ls3))


DEBUG:Going to execute:
(first [ is_ctor_list x | is_ctor_list y ]); inversion H; clear H
Level 4: x
 has value 
ls3

Level 4: Backtrace:

No matching clauses for match.
Level 3: Backtrace:

No matching clauses for match.
Level 3: evaluation
raised the exception
Backtrace:

No matching clauses for match.

Level 2: Backtrace:

No matching clauses for match.
Level 2: Backtrace:

No applicable tactic.
Level 2: Backtrace:

No applicable tactic.
Level 2: Backtrace:

No applicable tactic.