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
  ============================
   (All
      (λ z : B, All2_fold (λ (l1 l2 : list A) (x y : A), P l1 l2 x y z) [] [])
      ls1)


DEBUG:Going to execute:
congruence
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
Unable to unify "All ?M3046 (?M3047 :: ?M3048)" with 
"All ?P 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
Unable to unify "All ?M3046 (?M3047 :: ?M3048)" with 
"All ?P 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
Unable to unify "All ?M3046 (?M3047 :: ?M3048)" with 
"All ?P 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
Unable to unify "All ?M3046 (?M3047 :: ?M3048)" with 
"All ?P 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
Unable to unify "All ?M3046 (?M3047 :: ?M3048)" with 
"All ?P ls1".
Level 1: 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
Unable to unify "All ?M3046 (?M3047 :: ?M3048)" with 
"All ?P 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
Unable to unify "All ?M3046 (?M3047 :: ?M3048)" with 
"All ?P 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
Unable to unify "All ?M3046 (?M3047 :: ?M3048)" with 
"All ?P 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
Unable to unify "All ?M3046 (?M3047 :: ?M3048)" with 
"All ?P 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
Unable to unify "All ?M3046 (?M3047 :: ?M3048)" with 
"All ?P 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
Unable to unify "All ?M3046 (?M3047 :: ?M3048)" with 
"All ?P 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
Unable to unify "All ?M3046 (?M3047 :: ?M3048)" with 
"All ?P 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
Unable to unify "All ?M3046 (?M3047 :: ?M3048)" with 
"All ?P 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
Unable to unify "All ?M3046 (?M3047 :: ?M3048)" with 
"All ?P 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
Unable to unify "All ?M3046 (?M3047 :: ?M3048)" with 
"All ?P ls1".
Level 0: Backtrace:

No applicable tactic.