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
  X3 : All (λ x : A, Alli (P x) (S n) ls1) ls2
  X1 : P a0 n a
  X4 : All (λ x : A, P x n a) ls2
  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, Alli (P x) n (a :: ls1)) ls2)


DEBUG:Going to execute:
let H := multimatch goal with
                    | H:_ |- _ => H
                    end in
           eapply All_impl_All; [ exact H | clear H ]
Level 0: Backtrace:

In environment
A : Type
B : Type
P : A → nat → B → Type
a : A
ls2 : list A
n : nat
X : Alli (λ (n : nat) (y : B), All (λ x : A, P x n y) (a :: ls2)) n []
The term "A" has type "Type" 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 : A
ls2 : list A
n : nat
X : Alli (λ (n : nat) (y : B), All (λ x : A, P x n y) (a :: ls2)) n []
The term "A" has type "Type" 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 : A
ls2 : list A
n : nat
X : Alli (λ (n : nat) (y : B), All (λ x : A, P x n y) (a :: ls2)) n []
The term "A" has type "Type" 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 : A
ls2 : list A
n : nat
X : Alli (λ (n : nat) (y : B), All (λ x : A, P x n y) (a :: ls2)) n []
The term "A" has type "Type" 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 : A
ls2 : list A
n : nat
X : Alli (λ (n : nat) (y : B), All (λ x : A, P x n y) (a :: ls2)) n []
The term "A" has type "Type" 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 : A
ls2 : list A
n : nat
X : Alli (λ (n : nat) (y : B), All (λ x : A, P x n y) (a :: ls2)) n []
The term "A" has type "Type" 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 : A
ls2 : list A
n : nat
X : Alli (λ (n : nat) (y : B), All (λ x : A, P x n y) (a :: ls2)) n []
The term "A" has type "Type" while it is expected to have type "All ?P ls2".