Goal:
  
  A : Type
  P : list A → list A → A → A → Type
  n : nat
  Γ : list A
  a : 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 Γ (a :: 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)) Γ in
         let Γs' := skipn (S (S n)) (a :: 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