Inductive ord_opt {A} (ord: A -> A -> Prop): option A -> option A -> Prop:=
| Some_ord:
forall x y, ord x y -> ord_opt ord (Some x) (Some y).

(* Specifications: *)
Lemma option_wf:
forall A (ord: A -> A -> Prop),
well_founded ord ->
well_founded (ord_opt ord).