Goal:
  
  A : Type
  B : Type
  P : A → nat → B → Type
  a : B
  ls1 : list B
  a0 : A
  ls2 : list A
  n : nat
  X2 : Alli (P a0) (S n) ls1
  X1 : P a0 n a
  X0 : All (λ x : A, P x n a) (a0 :: ls2)
  X5 : Alli (λ (n : nat) (y : B), All (λ x : A, P x n y) (a0 :: ls2)) 
         (S n) ls1
  ============================
   (All
      (λ x : A,
         (λ x0 : A, Alli (P x0) (S n) ls1) x
         → P x n a → Alli (P x) n (a :: ls1)) ls2)


DEBUG:Going to execute:
H
Level 0: Backtrace:

In environment
A : Type
B : Type
P : A → nat → B → Type
a : B
ls1 : list B
a0 : A
ls2 : list A
n : nat
X2 : Alli (P a0) (S n) ls1
X1 : P a0 n a
X0 : All (λ x : A, P x n a) (a0 :: ls2)
X5 : Alli (λ (n : nat) (y : B), All (λ x : A, P x n y) (a0 :: ls2)) (S n) ls1
The term "ls2" has type "list A" while it is expected to have type
 "All ?P ls2".
Level 0: Backtrace:

In environment
A : Type
B : Type
P : A → nat → B → Type
a : B
ls1 : list B
a0 : A
ls2 : list A
n : nat
X2 : Alli (P a0) (S n) ls1
X1 : P a0 n a
X0 : All (λ x : A, P x n a) (a0 :: ls2)
X5 : Alli (λ (n : nat) (y : B), All (λ x : A, P x n y) (a0 :: ls2)) (S n) ls1
The term "ls2" has type "list A" while it is expected to have type
 "All ?P ls2".
Level 0: Backtrace:

In environment
A : Type
B : Type
P : A → nat → B → Type
a : B
ls1 : list B
a0 : A
ls2 : list A
n : nat
X2 : Alli (P a0) (S n) ls1
X1 : P a0 n a
X0 : All (λ x : A, P x n a) (a0 :: ls2)
X5 : Alli (λ (n : nat) (y : B), All (λ x : A, P x n y) (a0 :: ls2)) (S n) ls1
The term "ls2" has type "list A" while it is expected to have type
 "All ?P ls2".
Level 1: Backtrace:

In environment
A : Type
B : Type
P : A → nat → B → Type
a : B
ls1 : list B
a0 : A
ls2 : list A
n : nat
X2 : Alli (P a0) (S n) ls1
X1 : P a0 n a
X0 : All (λ x : A, P x n a) (a0 :: ls2)
X5 : Alli (λ (n : nat) (y : B), All (λ x : A, P x n y) (a0 :: ls2)) (S n) ls1
The term "ls2" has type "list A" while it is expected to have type
 "All ?P ls2".
Level 2: Backtrace:

In environment
A : Type
B : Type
P : A → nat → B → Type
a : B
ls1 : list B
a0 : A
ls2 : list A
n : nat
X2 : Alli (P a0) (S n) ls1
X1 : P a0 n a
X0 : All (λ x : A, P x n a) (a0 :: ls2)
X5 : Alli (λ (n : nat) (y : B), All (λ x : A, P x n y) (a0 :: ls2)) (S n) ls1
The term "ls2" has type "list A" while it is expected to have type
 "All ?P ls2".