Goal:
  
  A : Type
  P : list A → list A → A → A → Type
  n : nat
  a : A
  Γ : list A
  Γ' : list A
  d : A
  IHn : ∀ (Γ Γ' : list A) (d : A),
          All2_fold P Γ Γ'
          → nth_error Γ n = Some d
            → ∑ d' : A,
                nth_error Γ' n = Some d'
                × (let Γs := skipn (S n) Γ in
                   let Γs' := skipn (S n) Γ' in
                   All2_fold P Γs Γs' × P Γs Γs' d d')
  Hrel : All2_fold P (a :: Γ) Γ'
  H : nth_error (a :: Γ) (S n) = Some d
  ============================
   (∑ d' : A,
      nth_error Γ' (S n) = Some d'
      × (let Γs := skipn (S (S n)) (a :: Γ) in
         let Γs' := skipn (S (S n)) Γ' in All2_fold P Γs Γs' × P Γs Γs' d d'))


DEBUG:Going to execute:
fun id =>
             DepElim.do_depelim ltac:(fun hyp => DepElim.do_case hyp) id