Goal:
    A : Type  B : Type  P : A → nat → B → Type
  ============================
   (∀ (ls1 : list B) (ls2 : list A) (n : nat),
      All (λ x : A, Alli (P x) n ls1) ls2 <~>
      Alli (λ (n0 : nat) (y : B), All (λ x : A, P x n0 y) ls2) n ls1)


DEBUG:Going to execute:
induction ls1 as [| ? ? IH], ls2 as [| ? ls2] => n