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
  ============================
   (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)


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

In environment
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
Unable to unify "All ?M3203 (?M3204 :: ?M3205)" with
 "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".
Level 0: Backtrace:

In environment
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
Unable to unify "All ?M3203 (?M3204 :: ?M3205)" with
 "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".
Level 0: Backtrace:

In environment
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
Unable to unify "All ?M3203 (?M3204 :: ?M3205)" with
 "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".