Definition oboxopt Delta ret P :=
  match ret with
  | Some id => obox Delta id P
  | _ => P
  end.Definition odiaopt Delta ret P :=
  match ret with
  | Some id => odia Delta id P
  | _ => P
  end.Definition temp_guard_opt (Delta : tycontext) (i: option ident): Prop :=
  match i with
  | Some i => temp_guard Delta i
  | None => True
  end.

(* Specifications: *)
Lemma oboxopt_odiaopt: forall Delta i P, temp_guard_opt Delta i -> oboxopt Delta i (odiaopt Delta i P) = odiaopt Delta i P.