Goal:
  
  A : Type
  B : Type
  P : A → nat → B → Type
  a : B
  ls1 : list B
  a0 : A
  ls2 : list A
  n : nat
  X : Alli (λ (n : nat) (y : B), All (λ x : A, P x n y) (a0 :: ls2)) n
        (a :: ls1)
  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
  ============================
   (All (λ x : A, Alli (P x) n (a :: ls1)) ls2)


DEBUG:Going to execute:
match goal with
           | H:Alli _ _ (_ :: _) |- _ => inversion H; clear H; subst
           end
Level 0: Backtrace:

No matching clauses for match.