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
  X1 : 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
  X : All2_fold (λ (l1 l2 : list A) (x y : A), P l1 l2 x y a) ls2 ls3
  X2 : P ls2 ls3 a0 a1 a
  ============================
   (All2_fold (λ (l1 l2 : list A) (x y : A), All (P l1 l2 x y) (a :: ls1))
      ls2 ls3)


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,
       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
X1 : 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
X : All2_fold (λ (l1 l2 : list A) (x y : A), P l1 l2 x y a) ls2 ls3
X2 : P ls2 ls3 a0 a1 a
Unable to unify "All2_fold ?M3099 (?M3100 :: ?M3102) (?M3101 :: ?M3103)" with
 "All2_fold (λ (l1 l2 : list A) (x y : A), All (P l1 l2 x y) (a :: ls1)) ls2
    ls3".
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,
       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
X1 : 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
X : All2_fold (λ (l1 l2 : list A) (x y : A), P l1 l2 x y a) ls2 ls3
X2 : P ls2 ls3 a0 a1 a
Unable to unify "All2_fold ?M3099 (?M3100 :: ?M3102) (?M3101 :: ?M3103)" with
 "All2_fold (λ (l1 l2 : list A) (x y : A), All (P l1 l2 x y) (a :: ls1)) ls2
    ls3".
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,
       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
X1 : 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
X : All2_fold (λ (l1 l2 : list A) (x y : A), P l1 l2 x y a) ls2 ls3
X2 : P ls2 ls3 a0 a1 a
Unable to unify "All2_fold ?M3099 (?M3100 :: ?M3102) (?M3101 :: ?M3103)" with
 "All2_fold (λ (l1 l2 : list A) (x y : A), All (P l1 l2 x y) (a :: ls1)) ls2
    ls3".