Goal:
  
  A : Type
  P : list A → A → Type
  a : A
  Γ : list A
  Δ : list A
  IHΓ : ∀ Δ : list A,
          All_fold P (Γ ++ Δ)
          → All_fold P Δ × All_fold (λ Γ : list A, P (Γ ++ Δ)) Γ
  X : All_fold P ((a :: Γ) ++ Δ)
  ============================
   (All_fold (λ Γ : list A, P (Γ ++ Δ)) (a :: Γ))


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