Goal:
  
  A : Type
  B : Type
  P : A → nat → B → Type
  a : B
  ls1 : list B
  a0 : A
  ls2 : list A
  n : nat
  X1 : All (λ x : A, Alli (P x) n (a :: ls1)) ls2
  X3 : All (λ x : A, Alli (P x) n (a :: ls1)) ls2
  X : P a0 n a
  X4 : Alli (P a0) (S n) ls1
  X2 : P a0 n a
  X5 : Alli (P a0) (S n) ls1
  ============================
   (All (λ x : A, Alli (P x) (S n) ls1) ls2)


DEBUG:Going to execute:
repeat
            match goal with
            | |- ?X1 → ?X2 => intro
            | |- ¬ _ => unfold not at 1; intro
            end