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
  a0 : A
  ls2 : list A
  a1 : A
  ls3 : list A
  X0 : All2_fold (λ (l1 l2 : list A) (x y : A), All (P l1 l2 x y) (a :: ls1))
         ls2 ls3
  X : P ls2 ls3 a0 a1 a
  X2 : All (P ls2 ls3 a0 a1) ls1
  x : B
  ============================
   (All2_fold (λ (l1 l2 : list A) (x0 y : A), P l1 l2 x0 y x) ls2 ls3)


DEBUG:Going to execute:
contradiction
Level 1: Backtrace:

 The relation (All2_fold (λ (l1 l2 : list A) (x0 y : A), P l1 l2 x0 y x)) is not a declared symmetric relation. Maybe you need to require the Coq.Classes.RelationClasses library
Level 0: Backtrace:

 The relation (All2_fold (λ (l1 l2 : list A) (x0 y : A), P l1 l2 x0 y x)) is not a declared symmetric relation. Maybe you need to require the Coq.Classes.RelationClasses library
Level 0: Backtrace:

 The relation (All2_fold (λ (l1 l2 : list A) (x0 y : A), P l1 l2 x0 y x)) is not a declared symmetric relation. Maybe you need to require the Coq.Classes.RelationClasses library