Goal:
  
  A : Type
  B : Type
  P : A → nat → B → Type
  a : B
  ls1 : list B
  IH : ∀ (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
  n : nat
  X : All (λ x : A, Alli (P x) n (a :: ls1)) []
  ============================
   (Alli (λ (n : nat) (y : B), All (λ x : A, P x n y) []) (S n) ls1)


DEBUG:Going to execute:
apply IH; clear IH => //
Level 0: Backtrace:

The variable IH was not found in the current environment.
Level 0: Backtrace:

The variable IH was not found in the current environment.
Level 0: Backtrace:

The variable IH was not found in the current environment.