Goal:
  
  A : Type
  a : option A
  l : list (option A)
  f : A -> A
  l0 : list A
  IHl : map_option_out (map (option_map f) l) = Some (map f l0)
  a0 : A
  fa : option_map f a = Some a0
  ============================
   (Some (a0 :: map f l0) =
    option_map (map f)
      match a with
      | Some hd => Some (hd :: l0)
      | None => None
      end)


DEBUG:Going to execute:
destruct a; simpl in *
DEBUG LTAC Evaluated term: IHl
DEBUG LTAC Evaluated term: IHl
DEBUG LTAC Evaluated term: (map_option_out l)