Goal:
  
  A : Type
  P : A → Prop
  l' : list A
  a : A
  l : list (option A)
  p : on_Some_or_None P (Some a)
  X : All (on_Some_or_None P) l
  IHX : ∀ l' : list A, map_option_out l = Some l' → All P l'
  H : match map_option_out l with
      | Some tl => Some (a :: tl)
      | None => None
      end = Some l'
  H1 : match map_option_out l with
       | Some tl => Some (a :: tl)
       | None => None
       end = Some l'
  ============================
   (∀ l0 : list A, map_option_out l = Some l0 → All P l')


DEBUG:Going to execute:
intros l0 e; rewrite e in   H1; inversion H1